Qualitative data is subjective, rich, and in-depth information normally presented in the form of words. In undergraduate dissertations, the most common form of qualitative data is derived from semi-structured or unstructured interviews, although other sources can include observations, life histories and journals and documents of all kinds including newspapers.
Qualitative data from interviews can be analysed for content (content analysis) or for the language used (discourse analysis). Qualitative data is difficult to analyse and often opportunities to achieve high marks are lost because the data is treated casually and without rigour. Here we concentrate on the content analysis of data from interviews.
Theory
When using a quantitative methodology, you are normally testing theory through the testing of a hypothesis. In qualitative research, you are either exploring the application of a theory or model in a different context or are hoping for a theory or a model to emerge from the data. In other words, although you may have some ideas about your topic, you are also looking for ideas, concepts and attitudes often from experts or practitioners in the field.
Collecting and organising data
The means of collecting and recording data through interviews and the possible pitfalls are well documented elsewhere but in terms of subsequent analysis, it is essential that you have a complete and accurate record of what was said. Do not rely on your memory (it can be very selective!) and either tape record the conversation (preferably) or take copious notes. If you are taking notes, write them up straight after the interview so that you can elaborate and clarify. If you are using a tape recorder, transcribe the exact words onto paper.
However you record the data, you should end up with a hard copy of either exactly what was said (transcript of tape recording) or nearly exactly what was said (comprehensive notes). It may be that parts of the interview are irrelevant or are more in the nature of background material, in which case you need not put these into your transcript but do make sure that they are indeed unnecessary. You should indicate omissions in the text with short statements.
You should transcribe exactly what is said, with grammatical errors and so on. It does not look very authentic if all your respondents speak with perfect grammar and BBC English! You may also want to indicate other things that happen such as laughter.
Each transcript or set of notes should be clearly marked with the name of the interviewee, the date and place and any other relevant details and, where appropriate, cross-referenced to clearly labelled tapes. These transcripts and notes are not normally required to be included in your dissertation but they should be available to show your supervisor and the second marker if required.
You may wonder why you should go to all the bother of transcribing your audiotapes. It is certainly a time-consuming business, although much easier if you can get access to a transcription machine that enables you to start and stop the tape with your feet while carrying on typing. It is even easier if you have access to an audio-typist who will do this labour intensive part for you. The advantage of having the interviews etc in hard copy is that you can refer to them very quickly, make notes in the margins, re-organise them for analysis, make coding notations in the margins and so on. It is much slower in the long run to have to continually listen to the tapes. You can read much faster than the tape will play! It also has the advantage, especially if you do the transcription yourself, of ensuring that you are very familiar with the material.
Content analysis
Analysis of qualitative data is not simple, and although it does not require complicated statistical techniques of quantitative analysis, it is nonetheless difficult to handle the usually large amounts of data in a thorough, systematic and relevant manner. Marshall and Rossman offer this graphic description:
"Data analysis is the process of bringing order, structure and meaning to the mass of collected data. It is a messy, ambiguous, time-consuming, creative, and fascinating process. It does not proceed in a linear fashion; it is not neat. Qualitative data analysis is a search for general statements about relationships among categories of data."
Marshall and Rossman, 1990:111
Hitchcock and Hughes take this one step further:
"…the ways in which the researcher moves from a description of what is the case to an explanation of why what is the case is the case."
Hitchcock and Hughes 1995:295
Content analysis consists of reading and re-reading the transcripts looking for similarities and differences in order to find themes and to develop categories. Having the full transcript is essential to make sure that you do not leave out anything of importance by only selecting material that fits your own ideas. There are various ways that you can mark the text:
Coding paragraphs – This is where you mark each paragraph with a topic/theme/category with an appropriate word in the margin.
Highlighting paragraphs/sentences/phrases – This is where you use highlighter pens of different colours or different coloured pens to mark bits about the different themes. Using the example above, you could mark the bits relating to childcare and those relating to pay in a different colour, and so on. The use of coloured pens will help you find the relevant bits you need when you are writing up.
With both the above methods you may find that your categories change and develop as you do the analysis. What is important is that you can see that by analysing the text in such a way, you pick up all the references to a given topic and don’t leave anything out. This increases the objectivity and reduces the risk of you only selecting bits that conform to your own preconceptions.
You then need to arrange the data so that all the pieces on one theme are together. There are several ways of doing this:
• Cut and put in folders approach
Make several copies of each transcript (keeping the master safe) and cut up each one according to what is being discussed (your themes or categories). Then sort them into folders, one for each category, so that you have all together what each interviewee said about a given theme. You can then compare and look for similarities/differences/conclusions etc. Do not forget to mark each slip of paper with the respondent’s name, initials or some sort of code or you won’t be able to remember who said what. Several copies may be needed in case one paragraph contains more than one theme or category. This is time consuming and messy at first, but easier in the long run especially if you have a lot of data and categories.
• Card index system
Each transcript must be marked with line numbers for cross-referencing purposes. You have a card for each theme or category and cross-reference each card with each transcript so that you can find what everyone has said about a certain topic. This is quicker initially but involves a lot of referring back to the original transcripts when you write up your results and is usually only suitable for small amounts of data.
• Computer analysis
If you have access to a computer package that analyses qualitative data (e.g. NUDIST) then you can use this. These vary in the way they work but these are some of the basic common principles. You can upload your transcripts created in a compatible word-processing package and then the software allows you to mark different sections with various headings/themes. It will then sort all those sections marked with a particular heading and print them off together. This is the electronic version of the folders approach! It is also possible to use a word-processing package to cut and paste comments and to search for particular words.
There is a great danger of subjective interpretation. You must accurately reflect the views of the interviewees and be thorough and methodical. You need to become familiar with your data. You may find this a daunting and stressful task or you may really enjoy it – sometimes so much that you can delay getting down to the next stage which is interpreting and writing up!
Presenting qualitative data in your dissertation
This would normally follow the topics, themes and categories that you have developed in the analysis and these, in turn, are likely to have been themes that came out in the literature and may have formed the basis for your interview questions. It is usually a mistake to go through each interviewee in turn and what they said on each topic. This is cumbersome and does not give the scope to compare and contrast their ideas with the ideas of others.
Do not analyse the data on a question-by-question basis. You should summarise the key themes that emerge from the data and may give selected quotes if these are particularly appropriate.
Note how a point is made and then illustrated with an appropriate quote. The quotes make the whole text much more interesting and enjoyable to read but be wary of including too many. Please note also the reference to literature (this one is an imaginary piece of literature) – you should evaluate your own findings in this way and refer to the literature where appropriate. Remember the two concepts of presenting and discussing your findings. By presenting we mean a factual description/summary of what you found. The discussion element is your interpretation of what these findings mean and how they confirm or contradict what you wrote about in your literature section.
If you are trying to test a model then this will have been explored in your literature review and your methodology section will explain how you intend to test it. Your methodology should include who was interviewed with a clear rationale for your choices to explain how this fits into your research questions, how you ensured that the data was unbiased and as accurate as possible, and how the data was analysed. If you have been able to present an adapted model appropriate to your particular context then this should come towards the end of your findings section.
It may be desirable to put a small number of transcripts in the appendices but discuss this with your supervisor. Remember you have to present accurately what was said and what you think it means.
In order to write up your methodology section, you are strongly recommended to do some reading in research textbooks on interview techniques and the analysis of qualitative data. There are some suggested texts in the Further Reading section at the end of this pack.
Kamis, 12 Februari 2009
Rabu, 11 Februari 2009
SEM, Sebuah Kombinasi Dari Analisis Faktor - Syndi Octakomala D S (15406098)
Sejarah SEM
SEM adalah sebuah teknik pemodelan statistik yang sangat umum dan digunakan secara luas diberbagai lingkup ilmu pengetahuan. SEM dapat dilihat sebagai sebuah kombinasi dari analisis faktor (confirmatory factor analysis), dan regresi atau analisa alur (path analysis).
Pokok bahasan dalam SEM adalah konstruk teoritis yang digambarkan oleh faktor-faktor laten. Hubungan diantara konstruk teoritis tersebut digambarkan oleh regresi atau koefisien alur diantara berbagai faktor. SEM menunjukkan sebuah struktur bagi berbagai kovarian diantara variabel-variabel yang diobservasi, yang juga sering disebut dengan nama lain pemodelan struktur kovarian.
Namun demikian model tersebut dapat diperluas untuk memasukan rata-rata dari variabel yang diobservasi atau faktor dalam model. Banyak dari peneliti seringkali menyatakan pemodelan struktur kovarian sebagai model LISREL, yang mana penyebutan seperti di atas kurang tepat. Karena Lisrel merupakan kepanjangan dari LInear Structural RELationship yang juga merupakan salah satu program yang umum digunakan para peneliti untuk analisis SEM. Penggunaan nama Lisrel ini diberikan oleh Joreskog, sehubungan dengan program statistik untuk analisis SEM yang dikembangkan oleh Joreskog dengan nama yang sama (J.J. Hox dan T.M. Bechger, 2004).
Saat ini SEM tidak lagi hanya linear dan kemungkinan perluasan SEM akan melebihi program lisrel aslinya. SEM menyediakan kerangka kerja yang memenuhi dan sangat umum bagi analisa statistik yang mana termasuk didalamnya beberapa prosedur multivariat tradisional, sebagai contoh misalnya analisa faktor, analisa regresi, analisa diskriminan dan korelasi kanonikal sebagai kasus khusus.
SEM seringkali digambarkan oleh sebuah gambar diagram alur. Model ini didasarkan atas sistem persamaan linear yang pertama kali dikembangkan oleh Sewall Wright seorang ahli genetika tahun 1921 dalam studinya phylogenetic (Stoelting, 1992; Golob, 2001). Analisa alur ini kemudian diadopsi oleh ilmu-ilmu sosial sepanjang tahun 1960-an dan awal tahun 1970-an.
Para ahli sosiologi khususnya menemukan potensi analisa alur yang berhubungan dengan korelasi parsial. Analisa alur ini kemudian digantikan oleh SEM yang dikembangkan oleh Jöreskog (1970, 1973), Keesling (1972) dan Wiley (1973) yang dalam tulisan Bentler (1980) disebut sebagai JKW model. Model Jöreskog-Keesling-Wiley (JKW model) ini kemudian dianggap sebagai model SEM modern, yang kemudian populer dengan nama LISREL (Linear Structural Relationships) sebagai suatu program yang dikembangkan oleh Jöreskog (1970), Jöreskog, Gruvaeus dan van Thillo (1970), serta Jöreskog dan Sörbom (1979) seperti yang telah disinggung di depan.
Dalam model statistik, biasanya SEM ditampilkan dalam sebuah set persamaan matrik. Pada awal 1970-an ketika software LISREL untuk pertama kali diperkenalkan dalam penelitian, software ini membutuhkan penyesuaian untuk menyesuaikan model dalam hal matrik-matrik tersebut. Jadi para peneliti harus menyeleksi penggambaran matrik dari diagram alur, dan melengkapi software sebuah seri dari matrik untuk berbagai set parameter, seperti halnya faktor loading dan koefisien regresi. Pengembangan software terbaru memungkinkan peneliti untuk menentukan model langsung melalui diagram alur, seperti software yang dikembangkan oleh James L. Arbuckle (1995) yang dikenal dengan nama AMOS (Analysis of Moment Structures) (RumahStatistik).
SEM adalah sebuah teknik pemodelan statistik yang sangat umum dan digunakan secara luas diberbagai lingkup ilmu pengetahuan. SEM dapat dilihat sebagai sebuah kombinasi dari analisis faktor (confirmatory factor analysis), dan regresi atau analisa alur (path analysis).
Pokok bahasan dalam SEM adalah konstruk teoritis yang digambarkan oleh faktor-faktor laten. Hubungan diantara konstruk teoritis tersebut digambarkan oleh regresi atau koefisien alur diantara berbagai faktor. SEM menunjukkan sebuah struktur bagi berbagai kovarian diantara variabel-variabel yang diobservasi, yang juga sering disebut dengan nama lain pemodelan struktur kovarian.
Namun demikian model tersebut dapat diperluas untuk memasukan rata-rata dari variabel yang diobservasi atau faktor dalam model. Banyak dari peneliti seringkali menyatakan pemodelan struktur kovarian sebagai model LISREL, yang mana penyebutan seperti di atas kurang tepat. Karena Lisrel merupakan kepanjangan dari LInear Structural RELationship yang juga merupakan salah satu program yang umum digunakan para peneliti untuk analisis SEM. Penggunaan nama Lisrel ini diberikan oleh Joreskog, sehubungan dengan program statistik untuk analisis SEM yang dikembangkan oleh Joreskog dengan nama yang sama (J.J. Hox dan T.M. Bechger, 2004).
Saat ini SEM tidak lagi hanya linear dan kemungkinan perluasan SEM akan melebihi program lisrel aslinya. SEM menyediakan kerangka kerja yang memenuhi dan sangat umum bagi analisa statistik yang mana termasuk didalamnya beberapa prosedur multivariat tradisional, sebagai contoh misalnya analisa faktor, analisa regresi, analisa diskriminan dan korelasi kanonikal sebagai kasus khusus.
SEM seringkali digambarkan oleh sebuah gambar diagram alur. Model ini didasarkan atas sistem persamaan linear yang pertama kali dikembangkan oleh Sewall Wright seorang ahli genetika tahun 1921 dalam studinya phylogenetic (Stoelting, 1992; Golob, 2001). Analisa alur ini kemudian diadopsi oleh ilmu-ilmu sosial sepanjang tahun 1960-an dan awal tahun 1970-an.
Para ahli sosiologi khususnya menemukan potensi analisa alur yang berhubungan dengan korelasi parsial. Analisa alur ini kemudian digantikan oleh SEM yang dikembangkan oleh Jöreskog (1970, 1973), Keesling (1972) dan Wiley (1973) yang dalam tulisan Bentler (1980) disebut sebagai JKW model. Model Jöreskog-Keesling-Wiley (JKW model) ini kemudian dianggap sebagai model SEM modern, yang kemudian populer dengan nama LISREL (Linear Structural Relationships) sebagai suatu program yang dikembangkan oleh Jöreskog (1970), Jöreskog, Gruvaeus dan van Thillo (1970), serta Jöreskog dan Sörbom (1979) seperti yang telah disinggung di depan.
Dalam model statistik, biasanya SEM ditampilkan dalam sebuah set persamaan matrik. Pada awal 1970-an ketika software LISREL untuk pertama kali diperkenalkan dalam penelitian, software ini membutuhkan penyesuaian untuk menyesuaikan model dalam hal matrik-matrik tersebut. Jadi para peneliti harus menyeleksi penggambaran matrik dari diagram alur, dan melengkapi software sebuah seri dari matrik untuk berbagai set parameter, seperti halnya faktor loading dan koefisien regresi. Pengembangan software terbaru memungkinkan peneliti untuk menentukan model langsung melalui diagram alur, seperti software yang dikembangkan oleh James L. Arbuckle (1995) yang dikenal dengan nama AMOS (Analysis of Moment Structures) (RumahStatistik).
Selasa, 10 Februari 2009
Metode Kuantitatif dalam Pengambilan Keputusan -- Dimas Hartanto E 15406044
Secara umum, terdapat dua pendekatan dalam pengambilan keputusan, yaitu pendekatan kualitatif dan pendekatan kuantitatif.
Secara sederhana, pendekatan kualitatif mengandalkan penilaian subyektif terhadap suatu masalah, sedangkan pendekatan kuantitatif mendasarkan keputusan pada penilaian obyektif yang didasarkan pada model matematika yang dibuat. Jika Anda meramalkan cuaca mendasarkan pada pengalaman, maka pendekatan yang digunakan adalah kualitatif. Namun jika, ramalan didasarkan pada model matematika, maka pendekatan yang digunakan adalah kuantitatif. Keputusan penerimaan karyawan berdasar nilai tes masuk adalah contoh lain pendekatan kuantitatif, sedang jika didasarkan pada hasil wawancara untuk mengetahui kepribadian dan motivasi maka pendekatan yang dilakukan adalah kualitatif.
Umumnya pendekatan kuantitatif dalam pengambilan keputusan yang menggunakan model-model matematika. Matematika sudah ditemukan oleh manusia ribuan tahun yang lalu dan telah banyak digunakan dalam banyak aplikasi. Salah satu aplikasi matematika adalah untuk pengambilan keputusan. Sebagai contoh sederhana, bagaimana mengatur 50 kursi dengan ukuran tertentu ke dalam sebuah ruangan dengan ukuran tertentu pula. Dengan ukuran kursi dan ruangan, maka akan ditemukan cara terbaik untuk mengatur kursi; apakah 5 baris kali 10 lajur, atau sebaliknya, semuanya tergantung ukuran ruangan yang ada.
Untuk kasus yang lebih kompleks tentu saja dibutuhkan model matematika yang lebih rumit. Telah banyak model analisis kuantitatif yang dikembangkan dalam pengambilan keputusan.
Bagaimana prosesnya?
Secara umum, semua metode kuantitatif akan mengkonversikan data mentah menjadi informasi yang bermanfaat untuk pengambilan keputusan dari:
RAW MATERIAL -> ANALISIS KUANTITATIF -> INFORMASI YANG BERGUNA.
Sebagai contoh, dalam memproduksi produk A dan B, menggunakan bahan baku X, Y, Z, diketahui keuntungan penjualan produk A dan B. Angka yang menunjukkan banyak tiap bahan yang tersedia dan keuntungan dari tiap produk adalah data mentah. Analisis kuantitatif akan memproses data tersebut sehingga dihasilkan komposisi produksi (berapa banyak produk A dan B diproduksi) yang menghasilkan untuk optimal. Hasil inilah yang disebut denganinformasi yang bermanfaat untuk pengambilan keputusan.
Langkah-langkah dalam pengambilan keputusan
Mendefinisikan masalah. Secara sederhana, masalah merupakan perbedaan (gap) antara situasi yang diinginkan dengan kenyataan yang ada. Jika seorang mahasiswa ingin memperoleh nilai A, tetapi ternyata hasil yang didapatkan kurang dari itu, maka mahasiswa tersebut menghadapi masalah. Pada dasarnya, semua langkap pengambilan keputusan dilakukan untuk menghilangkan atau mengurangi perbedaan yang ada antara yang diharapkan dan yang terjadi.
Mengembangkan model. Model adalah representasi dari sebuah situasi nyata. Model dapat dikembangkan dalam berbagai bentuk; seperti model fisik, logika, atau matematika. Miniatur mobil atau maket rumah adalah contoh model fisik, sedang aliran listrik dengan rangkaian tertentu atau air mengalir dengan pola saluran tertentu adalah model logika untuk arus lalu-lintas. Model ekonomi yang menyatakan bahwa pendapatan merupakan fungsi dari konsumsi dan tabungan merupakan contoh model matematika.
Dalam langkah pengembangan model dikenal istilah variabel yang nilai-nilainya akan mempengaruhi keputusan yang akan diambil. Dalam kasus nyata, variabel-variabel ini sebagian dapat dikendalikan dan sebagian yang lain tidak. Lama lampu merah pada lampu pengatur lalu lintas dapat dikendalikan dengan mudah, namun laju kendaraan dan jumlah kendaraan yang melewati sebuah jalan tidak mudah dikendalikan.
Mengumpulkan data. Data yang akurat sangat penting untuk menjamin analisis kuantitatif yang dilakukan menghasilkan keluaran seperti yang diinginkan. Sumber data untuk pengujian model dapat berupa laporan-laporan perusahaan seperti laporan keuangan dan dokumen perusahaan lainnya, hasil wawancara, pengukuran langsung di lapangan dan hasilsampling statistik.
Membuat solusi. Solusi yang diambil dalam pendekatan kuantitatif dilakukan dengan memanipulasi model dan dengan masukan data yang dihasilkan pada langkah sebelumnya. Banyak metode yang bisa dilakukan dalam membuat solusi, seperti memecahkan persamaan (model matematika) yang sudah dikembangkan sebelumnya, menggunakan pendekatantrial and error dengan data masukan yang berbeda-beda untuk menghasilkan solusi ”terbaik”, atau menggunakan algoritma atau langkah-langkah penyelesaian detil khusus yang telah dikembangkan.
Apapun metode yang digunakan, solusi yang dihasilkan haruslah praktis (practical) dan dapat diterapkan (implementable). Solusi ”terbaik” yang dihasilkan harus tidak rumit dan dapat digunakan untuk memecahkan masalah yang ada.
Menguji solusi. Untuk menjamin bahwa solusi yang dihasilkan merupakan yang terbaik, maka pengujian harus dilakukan, baik pada model ataupun pada data masukan. Pengujian ini dilakukan untuk melihat akurasi (accuracy) dan kelengkapan model dan data yang digunakan. Untuk melihat akurasi dan kelengkapan data, data yang diperoleh dari berbagai sumber dapat dimasukkan ke dalam model dan hasilnya dibandingkan. Model dan data yang akurat dan lengkap seharusnya menjamin konsistensi hasil. Pengujian ini penting dilakukan sebelum analisis hasil dilakukan.
Menganalisis hasil. Analisis hasil dilakukan untuk memahami langkah-langkah yang harus dilakukan jika sebuah keputusan telah dipilih. Selanjutnya implikasi langkah-langkah yang dilalukan juga harus dianalisis. Dalam langkah ini analisis sensitivitas (sensitivity analysis) menjadi sangat penting. Analisis sensitivitas dilakukan dengan mengubah-ubah nilai-nilai masukan model dan melihat perbedaan apa yang terjadi pada hasil. Dengan demikian, analisis sensitivitas akan membantu untuk lebih memahami masalah yang dihadapi dan kemungkinan-kemungkinan jawaban atas masalah tersebut.
Mengimplementasikan hasil. Langkah implementasi ini dilakukan dengan menerapkan hasil analisis ke dalam proses-proses yang terdapat dalam perusahaan. Tidak kalah penting dalam langkah ini adalah memonitor hasil dari penerapan solusi. Namun, perlu disadari bahwa implementasi hasil analisis (solusi) bukanlah tanpa hambatan. Salah satu hambatan yang mungkin dihadapi adalah bagaimana meyakinkan pihak manajemen bahwa solusi yang ditawarkan merupakan yang terbaik dan akan memecahkan masalah yang ada. Dalam kasus ini, analisis sensitivitas atas model yang dihasilkan sekali lagi dapat digunakan untuk menjual solusi yang dihasilkan kepada pihak manajemen.
Secara sederhana, pendekatan kualitatif mengandalkan penilaian subyektif terhadap suatu masalah, sedangkan pendekatan kuantitatif mendasarkan keputusan pada penilaian obyektif yang didasarkan pada model matematika yang dibuat. Jika Anda meramalkan cuaca mendasarkan pada pengalaman, maka pendekatan yang digunakan adalah kualitatif. Namun jika, ramalan didasarkan pada model matematika, maka pendekatan yang digunakan adalah kuantitatif. Keputusan penerimaan karyawan berdasar nilai tes masuk adalah contoh lain pendekatan kuantitatif, sedang jika didasarkan pada hasil wawancara untuk mengetahui kepribadian dan motivasi maka pendekatan yang dilakukan adalah kualitatif.
Umumnya pendekatan kuantitatif dalam pengambilan keputusan yang menggunakan model-model matematika. Matematika sudah ditemukan oleh manusia ribuan tahun yang lalu dan telah banyak digunakan dalam banyak aplikasi. Salah satu aplikasi matematika adalah untuk pengambilan keputusan. Sebagai contoh sederhana, bagaimana mengatur 50 kursi dengan ukuran tertentu ke dalam sebuah ruangan dengan ukuran tertentu pula. Dengan ukuran kursi dan ruangan, maka akan ditemukan cara terbaik untuk mengatur kursi; apakah 5 baris kali 10 lajur, atau sebaliknya, semuanya tergantung ukuran ruangan yang ada.
Untuk kasus yang lebih kompleks tentu saja dibutuhkan model matematika yang lebih rumit. Telah banyak model analisis kuantitatif yang dikembangkan dalam pengambilan keputusan.
Bagaimana prosesnya?
Secara umum, semua metode kuantitatif akan mengkonversikan data mentah menjadi informasi yang bermanfaat untuk pengambilan keputusan dari:
RAW MATERIAL -> ANALISIS KUANTITATIF -> INFORMASI YANG BERGUNA.
Sebagai contoh, dalam memproduksi produk A dan B, menggunakan bahan baku X, Y, Z, diketahui keuntungan penjualan produk A dan B. Angka yang menunjukkan banyak tiap bahan yang tersedia dan keuntungan dari tiap produk adalah data mentah. Analisis kuantitatif akan memproses data tersebut sehingga dihasilkan komposisi produksi (berapa banyak produk A dan B diproduksi) yang menghasilkan untuk optimal. Hasil inilah yang disebut denganinformasi yang bermanfaat untuk pengambilan keputusan.
Langkah-langkah dalam pengambilan keputusan
Mendefinisikan masalah. Secara sederhana, masalah merupakan perbedaan (gap) antara situasi yang diinginkan dengan kenyataan yang ada. Jika seorang mahasiswa ingin memperoleh nilai A, tetapi ternyata hasil yang didapatkan kurang dari itu, maka mahasiswa tersebut menghadapi masalah. Pada dasarnya, semua langkap pengambilan keputusan dilakukan untuk menghilangkan atau mengurangi perbedaan yang ada antara yang diharapkan dan yang terjadi.
Mengembangkan model. Model adalah representasi dari sebuah situasi nyata. Model dapat dikembangkan dalam berbagai bentuk; seperti model fisik, logika, atau matematika. Miniatur mobil atau maket rumah adalah contoh model fisik, sedang aliran listrik dengan rangkaian tertentu atau air mengalir dengan pola saluran tertentu adalah model logika untuk arus lalu-lintas. Model ekonomi yang menyatakan bahwa pendapatan merupakan fungsi dari konsumsi dan tabungan merupakan contoh model matematika.
Dalam langkah pengembangan model dikenal istilah variabel yang nilai-nilainya akan mempengaruhi keputusan yang akan diambil. Dalam kasus nyata, variabel-variabel ini sebagian dapat dikendalikan dan sebagian yang lain tidak. Lama lampu merah pada lampu pengatur lalu lintas dapat dikendalikan dengan mudah, namun laju kendaraan dan jumlah kendaraan yang melewati sebuah jalan tidak mudah dikendalikan.
Mengumpulkan data. Data yang akurat sangat penting untuk menjamin analisis kuantitatif yang dilakukan menghasilkan keluaran seperti yang diinginkan. Sumber data untuk pengujian model dapat berupa laporan-laporan perusahaan seperti laporan keuangan dan dokumen perusahaan lainnya, hasil wawancara, pengukuran langsung di lapangan dan hasilsampling statistik.
Membuat solusi. Solusi yang diambil dalam pendekatan kuantitatif dilakukan dengan memanipulasi model dan dengan masukan data yang dihasilkan pada langkah sebelumnya. Banyak metode yang bisa dilakukan dalam membuat solusi, seperti memecahkan persamaan (model matematika) yang sudah dikembangkan sebelumnya, menggunakan pendekatantrial and error dengan data masukan yang berbeda-beda untuk menghasilkan solusi ”terbaik”, atau menggunakan algoritma atau langkah-langkah penyelesaian detil khusus yang telah dikembangkan.
Apapun metode yang digunakan, solusi yang dihasilkan haruslah praktis (practical) dan dapat diterapkan (implementable). Solusi ”terbaik” yang dihasilkan harus tidak rumit dan dapat digunakan untuk memecahkan masalah yang ada.
Menguji solusi. Untuk menjamin bahwa solusi yang dihasilkan merupakan yang terbaik, maka pengujian harus dilakukan, baik pada model ataupun pada data masukan. Pengujian ini dilakukan untuk melihat akurasi (accuracy) dan kelengkapan model dan data yang digunakan. Untuk melihat akurasi dan kelengkapan data, data yang diperoleh dari berbagai sumber dapat dimasukkan ke dalam model dan hasilnya dibandingkan. Model dan data yang akurat dan lengkap seharusnya menjamin konsistensi hasil. Pengujian ini penting dilakukan sebelum analisis hasil dilakukan.
Menganalisis hasil. Analisis hasil dilakukan untuk memahami langkah-langkah yang harus dilakukan jika sebuah keputusan telah dipilih. Selanjutnya implikasi langkah-langkah yang dilalukan juga harus dianalisis. Dalam langkah ini analisis sensitivitas (sensitivity analysis) menjadi sangat penting. Analisis sensitivitas dilakukan dengan mengubah-ubah nilai-nilai masukan model dan melihat perbedaan apa yang terjadi pada hasil. Dengan demikian, analisis sensitivitas akan membantu untuk lebih memahami masalah yang dihadapi dan kemungkinan-kemungkinan jawaban atas masalah tersebut.
Mengimplementasikan hasil. Langkah implementasi ini dilakukan dengan menerapkan hasil analisis ke dalam proses-proses yang terdapat dalam perusahaan. Tidak kalah penting dalam langkah ini adalah memonitor hasil dari penerapan solusi. Namun, perlu disadari bahwa implementasi hasil analisis (solusi) bukanlah tanpa hambatan. Salah satu hambatan yang mungkin dihadapi adalah bagaimana meyakinkan pihak manajemen bahwa solusi yang ditawarkan merupakan yang terbaik dan akan memecahkan masalah yang ada. Dalam kasus ini, analisis sensitivitas atas model yang dihasilkan sekali lagi dapat digunakan untuk menjual solusi yang dihasilkan kepada pihak manajemen.
Time Series Analysis - Indah Dwi Kartika 15406012
In the following topics, we will first review techniques used to identify patterns in time series data (such as smoothing and curve fitting techniques and autocorrelations), then we will introduce a general class of models that can be used to represent time series data and generate predictions (autoregressive and moving average models). Finally, we will review some simple but commonly used modeling and forecasting techniques based on linear regression. For more information on these topics, see the topic name below.
General Introduction
In the following topics, we will review techniques that are useful for analyzing time series data, that is, sequences of measurements that follow non-random orders. Unlike the analyses of random samples of observations that are discussed in the context of most other statistics, the analysis of time series is based on the assumption that successive values in the data file represent consecutive measurements taken at equally spaced time intervals.
Detailed discussions of the methods described in this section can be found in Anderson (1976), Box and Jenkins (1976), Kendall (1984), Kendall and Ord (1990), Montgomery, Johnson, and Gardiner (1990), Pankratz (1983), Shumway (1988), Vandaele (1983), Walker (1991), and Wei (1989).
Two Main Goals
There are two main goals of time series analysis: (a) identifying the nature of the phenomenon represented by the sequence of observations, and (b) forecasting (predicting future values of the time series variable). Both of these goals require that the pattern of observed time series data is identified and more or less formally described. Once the pattern is established, we can interpret and integrate it with other data (i.e., use it in our theory of the investigated phenomenon, e.g., sesonal commodity prices). Regardless of the depth of our understanding and the validity of our interpretation (theory) of the phenomenon, we can extrapolate the identified pattern to predict future events.
Identifying Patterns in Time Series Data :
- Systematic pattern and random noise
As in most other analyses, in time series analysis it is assumed that the data consist of a systematic pattern (usually a set of identifiable components) and random noise (error) which usually makes the pattern difficult to identify. Most time series analysis techniques involve some form of filtering out noise in order to make the pattern more salient.
- Two general aspects of time series patterns
Most time series patterns can be described in terms of two basic classes of components: trend and seasonality. The former represents a general systematic linear or (most often) nonlinear component that changes over time and does not repeat or at least does not repeat within the time range captured by our data (e.g., a plateau followed by a period of exponential growth). The latter may have a formally similar nature (e.g., a plateau followed by a period of exponential growth), however, it repeats itself in systematic intervals over time. Those two general classes of time series components may coexist in real-life data. For example, sales of a company can rapidly grow over years but they still follow consistent seasonal patterns (e.g., as much as 25% of yearly sales each year are made in December, whereas only 4% in August).
This general pattern is well illustrated in a "classic" Series G data set (Box and Jenkins, 1976, p. 531) representing monthly international airline passenger totals (measured in thousands) in twelve consecutive years from 1949 to 1960 (see example data file G.sta and graph above). If you plot the successive observations (months) of airline passenger totals, a clear, almost linear trend emerges, indicating that the airline industry enjoyed a steady growth over the years (approximately 4 times more passengers traveled in 1960 than in 1949). At the same time, the monthly figures will follow an almost identical pattern each year (e.g., more people travel during holidays then during any other time of the year). This example data file also illustrates a very common general type of pattern in time series data, where the amplitude of the seasonal changes increases with the overall trend (i.e., the variance is correlated with the mean over the segments of the series). This pattern which is called multiplicative seasonality indicates that the relative amplitude of seasonal changes is constant over time, thus it is related to the trend.
- Trend Analysis
There are no proven "automatic" techniques to identify trend components in the time series data; however, as long as the trend is monotonous (consistently increasing or decreasing) that part of data analysis is typically not very difficult. If the time series data contain considerable error, then the first step in the process of trend identification is smoothing.
Smoothing. Smoothing always involves some form of local averaging of data such that the nonsystematic components of individual observations cancel each other out. The most common technique is moving average smoothing which replaces each element of the series by either the simple or weighted average of n surrounding elements, where n is the width of the smoothing "window" (see Box & Jenkins, 1976; Velleman & Hoaglin, 1981). Medians can be used instead of means. The main advantage of median as compared to moving average smoothing is that its results are less biased by outliers (within the smoothing window). Thus, if there are outliers in the data (e.g., due to measurement errors), median smoothing typically produces smoother or at least more "reliable" curves than moving average based on the same window width. The main disadvantage of median smoothing is that in the absence of clear outliers it may produce more "jagged" curves than moving average and it does not allow for weighting.
In the relatively less common cases (in time series data), when the measurement error is very large, the distance weighted least squares smoothing or negative exponentially weighted smoothing techniques can be used. All those methods will filter out the noise and convert the data into a smooth curve that is relatively unbiased by outliers (see the respective sections on each of those methods for more details). Series with relatively few and systematically distributed points can be smoothed with bicubic splines.
Fitting a function. Many monotonous time series data can be adequately approximated by a linear function; if there is a clear monotonous nonlinear component, the data first need to be transformed to remove the nonlinearity. Usually a logarithmic, exponential, or (less often) polynomial function can be used.
- Analysis of Seasonality
Seasonal dependency (seasonality) is another general component of the time series pattern. The concept was illustrated in the example of the airline passengers data above. It is formally defined as correlational dependency of order k between each i'th element of the series and the (i-k)'th element (Kendall, 1976) and measured by autocorrelation (i.e., a correlation between the two terms); k is usually called the lag. If the measurement error is not too large, seasonality can be visually identified in the series as a pattern that repeats every k elements.
Autocorrelation correlogram. Seasonal patterns of time series can be examined via correlograms. The correlogram (autocorrelogram) displays graphically and numerically the autocorrelation function (ACF), that is, serial correlation coefficients (and their standard errors) for consecutive lags in a specified range of lags (e.g., 1 through 30). Ranges of two standard errors for each lag are usually marked in correlograms but typically the size of auto correlation is of more interest than its reliability (see Elementary Concepts) because we are usually interested only in very strong (and thus highly significant) autocorrelations.
Examining correlograms. While examining correlograms one should keep in mind that autocorrelations for consecutive lags are formally dependent. Consider the following example. If the first element is closely related to the second, and the second to the third, then the first element must also be somewhat related to the third one, etc. This implies that the pattern of serial dependencies can change considerably after removing the first order auto correlation (i.e., after differencing the series with a lag of 1).
Partial autocorrelations. Another useful method to examine serial dependencies is to examine the partial autocorrelation function (PACF) - an extension of autocorrelation, where the dependence on the intermediate elements (those within the lag) is removed. In other words the partial autocorrelation is similar to autocorrelation, except that when calculating it, the (auto) correlations with all the elements within the lag are partialled out (Box & Jenkins, 1976; see also McDowall, McCleary, Meidinger, & Hay, 1980). If a lag of 1 is specified (i.e., there are no intermediate elements within the lag), then the partial autocorrelation is equivalent to auto correlation. In a sense, the partial autocorrelation provides a "cleaner" picture of serial dependencies for individual lags (not confounded by other serial dependencies).
Removing serial dependency. Serial dependency for a particular lag of k can be removed by differencing the series, that is converting each i'th element of the series into its difference from the (i-k)''th element. There are two major reasons for such transformations.
First, one can identify the hidden nature of seasonal dependencies in the series. Remember that, as mentioned in the previous paragraph, autocorrelations for consecutive lags are interdependent. Therefore, removing some of the autocorrelations will change other auto correlations, that is, it may eliminate them or it may make some other seasonalities more apparent.
The other reason for removing seasonal dependencies is to make the series stationary which is necessary for ARIMA and other techniques.
General Introduction
In the following topics, we will review techniques that are useful for analyzing time series data, that is, sequences of measurements that follow non-random orders. Unlike the analyses of random samples of observations that are discussed in the context of most other statistics, the analysis of time series is based on the assumption that successive values in the data file represent consecutive measurements taken at equally spaced time intervals.
Detailed discussions of the methods described in this section can be found in Anderson (1976), Box and Jenkins (1976), Kendall (1984), Kendall and Ord (1990), Montgomery, Johnson, and Gardiner (1990), Pankratz (1983), Shumway (1988), Vandaele (1983), Walker (1991), and Wei (1989).
Two Main Goals
There are two main goals of time series analysis: (a) identifying the nature of the phenomenon represented by the sequence of observations, and (b) forecasting (predicting future values of the time series variable). Both of these goals require that the pattern of observed time series data is identified and more or less formally described. Once the pattern is established, we can interpret and integrate it with other data (i.e., use it in our theory of the investigated phenomenon, e.g., sesonal commodity prices). Regardless of the depth of our understanding and the validity of our interpretation (theory) of the phenomenon, we can extrapolate the identified pattern to predict future events.
Identifying Patterns in Time Series Data :
- Systematic pattern and random noise
As in most other analyses, in time series analysis it is assumed that the data consist of a systematic pattern (usually a set of identifiable components) and random noise (error) which usually makes the pattern difficult to identify. Most time series analysis techniques involve some form of filtering out noise in order to make the pattern more salient.
- Two general aspects of time series patterns
Most time series patterns can be described in terms of two basic classes of components: trend and seasonality. The former represents a general systematic linear or (most often) nonlinear component that changes over time and does not repeat or at least does not repeat within the time range captured by our data (e.g., a plateau followed by a period of exponential growth). The latter may have a formally similar nature (e.g., a plateau followed by a period of exponential growth), however, it repeats itself in systematic intervals over time. Those two general classes of time series components may coexist in real-life data. For example, sales of a company can rapidly grow over years but they still follow consistent seasonal patterns (e.g., as much as 25% of yearly sales each year are made in December, whereas only 4% in August).
This general pattern is well illustrated in a "classic" Series G data set (Box and Jenkins, 1976, p. 531) representing monthly international airline passenger totals (measured in thousands) in twelve consecutive years from 1949 to 1960 (see example data file G.sta and graph above). If you plot the successive observations (months) of airline passenger totals, a clear, almost linear trend emerges, indicating that the airline industry enjoyed a steady growth over the years (approximately 4 times more passengers traveled in 1960 than in 1949). At the same time, the monthly figures will follow an almost identical pattern each year (e.g., more people travel during holidays then during any other time of the year). This example data file also illustrates a very common general type of pattern in time series data, where the amplitude of the seasonal changes increases with the overall trend (i.e., the variance is correlated with the mean over the segments of the series). This pattern which is called multiplicative seasonality indicates that the relative amplitude of seasonal changes is constant over time, thus it is related to the trend.
- Trend Analysis
There are no proven "automatic" techniques to identify trend components in the time series data; however, as long as the trend is monotonous (consistently increasing or decreasing) that part of data analysis is typically not very difficult. If the time series data contain considerable error, then the first step in the process of trend identification is smoothing.
Smoothing. Smoothing always involves some form of local averaging of data such that the nonsystematic components of individual observations cancel each other out. The most common technique is moving average smoothing which replaces each element of the series by either the simple or weighted average of n surrounding elements, where n is the width of the smoothing "window" (see Box & Jenkins, 1976; Velleman & Hoaglin, 1981). Medians can be used instead of means. The main advantage of median as compared to moving average smoothing is that its results are less biased by outliers (within the smoothing window). Thus, if there are outliers in the data (e.g., due to measurement errors), median smoothing typically produces smoother or at least more "reliable" curves than moving average based on the same window width. The main disadvantage of median smoothing is that in the absence of clear outliers it may produce more "jagged" curves than moving average and it does not allow for weighting.
In the relatively less common cases (in time series data), when the measurement error is very large, the distance weighted least squares smoothing or negative exponentially weighted smoothing techniques can be used. All those methods will filter out the noise and convert the data into a smooth curve that is relatively unbiased by outliers (see the respective sections on each of those methods for more details). Series with relatively few and systematically distributed points can be smoothed with bicubic splines.
Fitting a function. Many monotonous time series data can be adequately approximated by a linear function; if there is a clear monotonous nonlinear component, the data first need to be transformed to remove the nonlinearity. Usually a logarithmic, exponential, or (less often) polynomial function can be used.
- Analysis of Seasonality
Seasonal dependency (seasonality) is another general component of the time series pattern. The concept was illustrated in the example of the airline passengers data above. It is formally defined as correlational dependency of order k between each i'th element of the series and the (i-k)'th element (Kendall, 1976) and measured by autocorrelation (i.e., a correlation between the two terms); k is usually called the lag. If the measurement error is not too large, seasonality can be visually identified in the series as a pattern that repeats every k elements.
Autocorrelation correlogram. Seasonal patterns of time series can be examined via correlograms. The correlogram (autocorrelogram) displays graphically and numerically the autocorrelation function (ACF), that is, serial correlation coefficients (and their standard errors) for consecutive lags in a specified range of lags (e.g., 1 through 30). Ranges of two standard errors for each lag are usually marked in correlograms but typically the size of auto correlation is of more interest than its reliability (see Elementary Concepts) because we are usually interested only in very strong (and thus highly significant) autocorrelations.
Examining correlograms. While examining correlograms one should keep in mind that autocorrelations for consecutive lags are formally dependent. Consider the following example. If the first element is closely related to the second, and the second to the third, then the first element must also be somewhat related to the third one, etc. This implies that the pattern of serial dependencies can change considerably after removing the first order auto correlation (i.e., after differencing the series with a lag of 1).
Partial autocorrelations. Another useful method to examine serial dependencies is to examine the partial autocorrelation function (PACF) - an extension of autocorrelation, where the dependence on the intermediate elements (those within the lag) is removed. In other words the partial autocorrelation is similar to autocorrelation, except that when calculating it, the (auto) correlations with all the elements within the lag are partialled out (Box & Jenkins, 1976; see also McDowall, McCleary, Meidinger, & Hay, 1980). If a lag of 1 is specified (i.e., there are no intermediate elements within the lag), then the partial autocorrelation is equivalent to auto correlation. In a sense, the partial autocorrelation provides a "cleaner" picture of serial dependencies for individual lags (not confounded by other serial dependencies).
Removing serial dependency. Serial dependency for a particular lag of k can be removed by differencing the series, that is converting each i'th element of the series into its difference from the (i-k)''th element. There are two major reasons for such transformations.
First, one can identify the hidden nature of seasonal dependencies in the series. Remember that, as mentioned in the previous paragraph, autocorrelations for consecutive lags are interdependent. Therefore, removing some of the autocorrelations will change other auto correlations, that is, it may eliminate them or it may make some other seasonalities more apparent.
The other reason for removing seasonal dependencies is to make the series stationary which is necessary for ARIMA and other techniques.
Model Analisis Peramalan (FORECASTING) - Said Wahyudhi Berry Murja 15406028
MODEL ANALISIS PERAMALAN (FORECASTING)
Metode sistem peramalan yang sering digunakan dapat dilihat pada gambar di bawah ini (Makrdakis, 1999)
METODE SISTEM PERAMALAN (Maksdakis, 1999)
1. Metode Deret Waktu (Time series Method)
Metode peramalan ini menggunakan deret waktu (time series) sebagai dasar peramalan.perlukan data aktual lalu yang akan diramalkan untuk mengetahui pola data yang diperlukan untuk menentukan metode peramalan yang sesuai. Beberapa metode dalam time series yaitu sebagai berikut:
• ARIMA (Autoregressive Integrated Moving Average) pada dasarnya menggunakan fungsi deret waktu, metode ini memerlukan pendekatan model identification serta penaksiran awal dari paramaternya. Sebagai contoh: peramalan nilai tukar mata uang asing, pergerakan nilai IHSG.
• Kalman Filter banyak digunakan pada bidang rekayasa sistem untuk memisahkan sinyal dari noise yang masuk ke sistem. Metoda ini menggunakan pendekatan model state space dengan asumsi white noise memiliki distribusi Gaussian.
• Bayesian merupakan metode yang menggunakan state space berdasarkan model dinamis linear (dynamical linear model). Sebagai contoh: menentukan diagnosa suatu penyakit berdasarkan data-data gejala (hipertensi atau sakit jantung), mengenali warna berdasarkan fitur indeks warna RGB, mendeteksi warna kulit (skin detection) berdasarkan fitur warna chrominant.
• Metode smoothing dipakai untuk mengurangi ketidakteraturan data yang bersifat musiman dengan cara membuat keseimbangan rata-rata dari data masa lampau.
• Regresi menggunakan dummy variabel dalam formulasi matematisnya. Sebagai contoh: kemampuan dalam meramal sales suatu produk berdasarkan harganya.
2. Metode Kausal
Metode ini menggunakan pendekatan sebab-akibat, dan bertujuan untuk meramalkan keadaan di masa yang akan datang dengan menemukan dan mengukur beberapa variabel bebas (independen) yang penting beserta pengaruhnya terhadap variabel tidak bebas yang akan diramalkan. Pada metode kausal terdapat tiga kelompok metode yang sering dipakai yaitu :
• Metoda regresi dan korelasi memakai teknik kuadrat terkecil (least square). Metoda ini sering digunakan untuk prediksi jangka pendek. Contohnya: meramalkan hubungan jumlah kredit yang diberikan dengan giro, deposito dan tabungan masyarakat.
• Metoda ekonometri berdasarkan pada persamaan regresi yang didekati secara simultan. Metoda ini sering digunakan untuk perencanaan ekonomi nasional dalam jangka pendek maupun jangka panjang. Contohnya: meramalkan besarnya indikator moneter buat beberapa tahun ke depan, hal ini sering dilakukan pihak BI tiap tahunnya.
• Metoda input output biasa digunakan untuk perencanaan ekonomi nasional jangka panjang. Contohnya: meramalkan pertumbuhan ekonomi seperti pertumbuhan domestik bruto (PDB) untuk beberapa periode tahun ke depan 5-10 tahun mendatang.
Secara ringkas terdapat tiga tahapan yang harus dilalui dalam perancangan suatu metoda peramalan, yaitu :
a. Melakukan analisa pada data masa lampau. Langkah ini bertujuan untuk mendapatkan gambaran pola dari data bersangkutan;
b. Memilih metoda yang akan digunakan. Terdapat bermacam-macam metoda yang tersedia dengan keperluannya. Metoda yang berlainan akan menghasilkan system prediksi yang berbeda pula untuk data yang sama. Secara umum dapat dikatakan bahwa metoda yang berhasil adalah metoda yang menghasilkan penyimpangan (error) sekecil-kecilnya antara hasil prediksi dengan kenyataan yang terjadi;
c. Proses transformasi dari data masa lampau dengan menggunakan metoda yang dipilih. Kalau diperlukan, diadakan perubahan sesuai kebutuhannya. Menurut John E. Hanke dan Arthur G. Reitch (1995), metode peramalan dapat dibagi menjadi dua yakni :
Metode peramalan kualitatif atau subyektif :
“Qualitative forecasting techniques relied on human judgments and intuition more than manipulation of past historical data,” atau metode yang hanya didasarkan kepada penilaian dan intuisi, bukan kepada pengolahan data historis.
Metode Peramalan Kuantitatif
Sedangkan peramalan kuantitatif diterangkan sebagai : “quantitative techniques that need no input of judgments; they are mechanical procedures that produce quantitative result and some quantitative procedures require a much more sophisticated manipulation of data than do other, of course”. Sedangkan De Lurgio (1998) mengilustrasikan jenis-jenis metode peramalan seperti pada Gambar berikut:
JENIS-JENIS METODE PERAMALAN (De Lurgio, 1998)
(sumber : http://www.ittelkom.ac.id/library/index.php?view=article&catid=25%3Aindustri&id=258%3Ametode-peramalan-forecasting-method&option=com_content&Itemid=15)
Metode sistem peramalan yang sering digunakan dapat dilihat pada gambar di bawah ini (Makrdakis, 1999)
METODE SISTEM PERAMALAN (Maksdakis, 1999)
1. Metode Deret Waktu (Time series Method)
Metode peramalan ini menggunakan deret waktu (time series) sebagai dasar peramalan.perlukan data aktual lalu yang akan diramalkan untuk mengetahui pola data yang diperlukan untuk menentukan metode peramalan yang sesuai. Beberapa metode dalam time series yaitu sebagai berikut:
• ARIMA (Autoregressive Integrated Moving Average) pada dasarnya menggunakan fungsi deret waktu, metode ini memerlukan pendekatan model identification serta penaksiran awal dari paramaternya. Sebagai contoh: peramalan nilai tukar mata uang asing, pergerakan nilai IHSG.
• Kalman Filter banyak digunakan pada bidang rekayasa sistem untuk memisahkan sinyal dari noise yang masuk ke sistem. Metoda ini menggunakan pendekatan model state space dengan asumsi white noise memiliki distribusi Gaussian.
• Bayesian merupakan metode yang menggunakan state space berdasarkan model dinamis linear (dynamical linear model). Sebagai contoh: menentukan diagnosa suatu penyakit berdasarkan data-data gejala (hipertensi atau sakit jantung), mengenali warna berdasarkan fitur indeks warna RGB, mendeteksi warna kulit (skin detection) berdasarkan fitur warna chrominant.
• Metode smoothing dipakai untuk mengurangi ketidakteraturan data yang bersifat musiman dengan cara membuat keseimbangan rata-rata dari data masa lampau.
• Regresi menggunakan dummy variabel dalam formulasi matematisnya. Sebagai contoh: kemampuan dalam meramal sales suatu produk berdasarkan harganya.
2. Metode Kausal
Metode ini menggunakan pendekatan sebab-akibat, dan bertujuan untuk meramalkan keadaan di masa yang akan datang dengan menemukan dan mengukur beberapa variabel bebas (independen) yang penting beserta pengaruhnya terhadap variabel tidak bebas yang akan diramalkan. Pada metode kausal terdapat tiga kelompok metode yang sering dipakai yaitu :
• Metoda regresi dan korelasi memakai teknik kuadrat terkecil (least square). Metoda ini sering digunakan untuk prediksi jangka pendek. Contohnya: meramalkan hubungan jumlah kredit yang diberikan dengan giro, deposito dan tabungan masyarakat.
• Metoda ekonometri berdasarkan pada persamaan regresi yang didekati secara simultan. Metoda ini sering digunakan untuk perencanaan ekonomi nasional dalam jangka pendek maupun jangka panjang. Contohnya: meramalkan besarnya indikator moneter buat beberapa tahun ke depan, hal ini sering dilakukan pihak BI tiap tahunnya.
• Metoda input output biasa digunakan untuk perencanaan ekonomi nasional jangka panjang. Contohnya: meramalkan pertumbuhan ekonomi seperti pertumbuhan domestik bruto (PDB) untuk beberapa periode tahun ke depan 5-10 tahun mendatang.
Secara ringkas terdapat tiga tahapan yang harus dilalui dalam perancangan suatu metoda peramalan, yaitu :
a. Melakukan analisa pada data masa lampau. Langkah ini bertujuan untuk mendapatkan gambaran pola dari data bersangkutan;
b. Memilih metoda yang akan digunakan. Terdapat bermacam-macam metoda yang tersedia dengan keperluannya. Metoda yang berlainan akan menghasilkan system prediksi yang berbeda pula untuk data yang sama. Secara umum dapat dikatakan bahwa metoda yang berhasil adalah metoda yang menghasilkan penyimpangan (error) sekecil-kecilnya antara hasil prediksi dengan kenyataan yang terjadi;
c. Proses transformasi dari data masa lampau dengan menggunakan metoda yang dipilih. Kalau diperlukan, diadakan perubahan sesuai kebutuhannya. Menurut John E. Hanke dan Arthur G. Reitch (1995), metode peramalan dapat dibagi menjadi dua yakni :
Metode peramalan kualitatif atau subyektif :
“Qualitative forecasting techniques relied on human judgments and intuition more than manipulation of past historical data,” atau metode yang hanya didasarkan kepada penilaian dan intuisi, bukan kepada pengolahan data historis.
Metode Peramalan Kuantitatif
Sedangkan peramalan kuantitatif diterangkan sebagai : “quantitative techniques that need no input of judgments; they are mechanical procedures that produce quantitative result and some quantitative procedures require a much more sophisticated manipulation of data than do other, of course”. Sedangkan De Lurgio (1998) mengilustrasikan jenis-jenis metode peramalan seperti pada Gambar berikut:
JENIS-JENIS METODE PERAMALAN (De Lurgio, 1998)
(sumber : http://www.ittelkom.ac.id/library/index.php?view=article&catid=25%3Aindustri&id=258%3Ametode-peramalan-forecasting-method&option=com_content&Itemid=15)
Senin, 09 Februari 2009
factor analysis by Novian_15407025
Factor analysis is used to uncover the latent structure (dimensions) of a set of variables. It reduces attribute space from a larger number of variables to a smaller number of factors and as such is a "non-dependent" procedure (that is, it does not assume a dependent variable is specified). Factor analysis could be used for any of the following purposes:
To reduce a large number of variables to a smaller number of factors for modeling purposes, where the large number of variables precludes modeling all the measures individually. As such, factor analysis is integrated in structural equation modeling (SEM), helping confirm the latent variables modeled by SEM. However, factor analysis can be and is often used on a stand-alone basis for similar purposes.
To establish that multiple tests measure the same factor, thereby giving justification for administering fewer tests. Factor analysis originated a century ago with Charles Spearman's attempts to show that a wide variety of mental tests could be explained by a single underlying intelligence factor (a notion now rejected, by the way).
To validate a scale or index by demonstrating that its constituent items load on the same factor, and to drop proposed scale items which cross-load on more than one factor.
To select a subset of variables from a larger set, based on which original variables have the highest correlations with the principal component factors.
To create a set of factors to be treated as uncorrelated variables as one approach to handling multicollinearity in such procedures as multiple regression
To identify clusters of cases and/or outliers.
To determine network groups by determining which sets of people cluster together (using Q-mode factor analysis, discussed below)
A non-technical analogy: A mother sees various bumps and shapes under a blanket at the bottom of a bed. When one shape moves toward the top of the bed, all the other bumps and shapes move toward the top also, so the mother concludes that what is under the blanket is a single thing, most likely her child. Similarly, factor analysis takes as input a number of measures and tests, analogous to the bumps and shapes. Those that move together are considered a single thing, which it labels a factor. That is, in factor analysis the researcher is assuming that there is a "child" out there in the form of an underlying factor, and he or she takes simultaneous movement (correlation) as evidence of its existence. If correlation is spurious for some reason, this inference will be mistaken, of course, so it is important when conducting factor analysis that possible variables which might introduce spuriousness, such as anteceding causes, be included in the analysis and taken into account.
Factor analysis is part of the general linear model (GLM) family of procedures and makes many of the same assumptions as multiple regression: linear relationships, interval or near-interval data, untruncated variables, proper specification (relevant variables included, extraneous ones excluded), lack of high multicollinearity, and multivariate normality for purposes of significance testing. Factor analysis generates a table in which the rows are the observed raw indicator variables and the columns are the factors or latent variables which explain as much of the variance in these variables as possible. The cells in this table are factor loadings, and the meaning of the factors must be induced from seeing which variables are most heavily loaded on which factors. This inferential labeling process can be fraught with subjectivity as diverse researchers impute different labels.
There are several different types of factor analysis, with the most common being principal components analysis (PCA), which is preferred for purposes of data reduction. However, common factor analysis is preferred for purposes of causal analysis anf for confirmatory factor analysis in structural equation modeling, among other settings..
To reduce a large number of variables to a smaller number of factors for modeling purposes, where the large number of variables precludes modeling all the measures individually. As such, factor analysis is integrated in structural equation modeling (SEM), helping confirm the latent variables modeled by SEM. However, factor analysis can be and is often used on a stand-alone basis for similar purposes.
To establish that multiple tests measure the same factor, thereby giving justification for administering fewer tests. Factor analysis originated a century ago with Charles Spearman's attempts to show that a wide variety of mental tests could be explained by a single underlying intelligence factor (a notion now rejected, by the way).
To validate a scale or index by demonstrating that its constituent items load on the same factor, and to drop proposed scale items which cross-load on more than one factor.
To select a subset of variables from a larger set, based on which original variables have the highest correlations with the principal component factors.
To create a set of factors to be treated as uncorrelated variables as one approach to handling multicollinearity in such procedures as multiple regression
To identify clusters of cases and/or outliers.
To determine network groups by determining which sets of people cluster together (using Q-mode factor analysis, discussed below)
A non-technical analogy: A mother sees various bumps and shapes under a blanket at the bottom of a bed. When one shape moves toward the top of the bed, all the other bumps and shapes move toward the top also, so the mother concludes that what is under the blanket is a single thing, most likely her child. Similarly, factor analysis takes as input a number of measures and tests, analogous to the bumps and shapes. Those that move together are considered a single thing, which it labels a factor. That is, in factor analysis the researcher is assuming that there is a "child" out there in the form of an underlying factor, and he or she takes simultaneous movement (correlation) as evidence of its existence. If correlation is spurious for some reason, this inference will be mistaken, of course, so it is important when conducting factor analysis that possible variables which might introduce spuriousness, such as anteceding causes, be included in the analysis and taken into account.
Factor analysis is part of the general linear model (GLM) family of procedures and makes many of the same assumptions as multiple regression: linear relationships, interval or near-interval data, untruncated variables, proper specification (relevant variables included, extraneous ones excluded), lack of high multicollinearity, and multivariate normality for purposes of significance testing. Factor analysis generates a table in which the rows are the observed raw indicator variables and the columns are the factors or latent variables which explain as much of the variance in these variables as possible. The cells in this table are factor loadings, and the meaning of the factors must be induced from seeing which variables are most heavily loaded on which factors. This inferential labeling process can be fraught with subjectivity as diverse researchers impute different labels.
There are several different types of factor analysis, with the most common being principal components analysis (PCA), which is preferred for purposes of data reduction. However, common factor analysis is preferred for purposes of causal analysis anf for confirmatory factor analysis in structural equation modeling, among other settings..
quantitative analyst by maylano_15407109
A quantitative analyst is a person who works in finance using numerical or quantitative techniques. Similar work is done in most other modern industries, but the work is not called quantitative analysis. In the investment industry, people who perform quantitative analysis are frequently called quants.
Although the original quants were concerned with risk management and derivatives pricing, the meaning of the term has expanded over time to include those individuals involved in almost any application of mathematics in finance. An example is statistical arbitrage.
Contents
[hide] [hide]
* 1 History
* 2 Education
* 3 Front Office Quant
* 4 Mathematical and statistical approaches
* 5 Seminal publications
* 6 References
* 7 External links
[edit] History
Robert C. Merton, a pioneer of quantitative analysis, introduced stochastic calculus into the study of finance.
Quantitative finance started in the U.S. in the 1930s as some astute investors began using mathematical formulae to price stocks and bonds.
Harry Markowitz's 1952 Ph.D thesis "Portfolio Selection" was one of the first papers to formally adapt mathematical concepts to finance. Markowitz formalized a notion of mean return and covariances for common stocks which allowed him to quantify the concept of "diversification" in a market. He showed how to compute the mean return and variance for a given portfolio and argued that investors should hold only those portfolios whose variance is minimal among all portfolios with a given mean return. Although the language of finance now involves Itō calculus, minimization of risk in a quantifiable manner underlies much of the modern theory.
In 1969 Robert Merton introduced stochastic calculus into the study of finance. Merton was motivated by the desire to understand how prices are set in financial markets, which is the classical economics question of "equilibrium," and in later papers he used the machinery of stochastic calculus to begin investigation of this issue.
At the same time as Merton's work and with Merton's assistance, Fischer Black and Myron Scholes were developing their option pricing formula, which led to winning the 1997 Nobel Prize in Economics. It provided a solution for a practical problem, that of finding a fair price for a European call option, i.e., the right to buy one share of a given stock at a specified price and time. Such options are frequently purchased by investors as a risk-hedging device. In 1981, Harrison and Pliska used the general theory of continuous-time stochastic processes to put the Black-Scholes option pricing formula on a solid theoretical basis, and as a result, showed how to price numerous other "derivative" securities.
[edit] Education
Quants often come from physics or mathematics backgrounds rather than finance related fields, and quants are a major source of employment for people with physics and mathematics Ph.D's. Typically, a quant will also need extensive skills in computer programming.
This demand for quants has led to the creation of specialized Masters and PhD courses in mathematical finance, computational finance, and/or financial reinsurance. In particular, Masters degrees in financial engineering and financial analysis are becoming more popular with students and with employers. London's Cass Business School was the pioneer of quantitative finance programs in Europe, with its MSc Quantitative Finance as well as the MSc Financial Mathematics and MSc Mathematical Trading and Finance programs providing some leading global research. Carnegie Mellon's Tepper School of Business, which created the Masters degree in financial engineering, reported a 21% increase in applicants to their MS in Computational Finance program, which is on top of a 48% increase in the year before.[1][when?] These Masters level programs are generally one year in length and more focused than the broader MBA degree.
[edit] Front Office Quant
Within Banking, quants are employed to support trading and sales functions. At the very simple level Banks buy and sell investment products known as Stocks (Equity) and Bonds (Debt). They can gain a good idea of a fair price to charge for these because they are liquid instruments (many people are buying and selling them) and thus they are governed by the market principles of supply and demand – the lower your price the more people will buy from you, the higher your price the more people will sell to you. Over the last 30 years a massive industry in derivative securities has developed as the risk preferences and profiles of customers have matured. The idiosyncratic, customised nature of many of these products can make them relatively illiquid and hence there are no handy market prices available. The products are managed, that is, actualised, priced and hedged, by means of financial models. The models are implemented as software and then embedded in front-office risk management systems. The role of the quant is to develop these models.
[edit] Mathematical and statistical approaches
According to Fund of Funds analyst Fred Gehm, "There are two types of quantitative analysis and, therefore, two types of quants. One type works primarily with mathematical models and the other primarily with statistical models. While there is no logical reason why one person can't do both kinds of work, this doesn’t seem to happen, perhaps because these types demand different skill sets and, much more important, different psychologies.[2]"
A typical problem for a numerically oriented quantitative analyst would be to develop a model for pricing and managing a complex derivative product.
A typical problem for statistically oriented quantitative analyst would be to develop a model for deciding which stocks are relatively expensive and which stocks are relatively cheap. The model might include a company's book value to price ratio, its trailing earnings to price ratio and other accounting factors. An investment manager might implement this analysis by buying the underpriced stocks, selling the overpriced stocks or both.
One of the principal mathematical tools of quantitative finance is stochastic calculus.
According to a July 2008 Aite Group report, today quants often use alpha generation platforms to help them develop financial models. These software solutions enable quants to centralize and streamline the alpha generation process.[3]
Although the original quants were concerned with risk management and derivatives pricing, the meaning of the term has expanded over time to include those individuals involved in almost any application of mathematics in finance. An example is statistical arbitrage.
Contents
[hide] [hide]
* 1 History
* 2 Education
* 3 Front Office Quant
* 4 Mathematical and statistical approaches
* 5 Seminal publications
* 6 References
* 7 External links
[edit] History
Robert C. Merton, a pioneer of quantitative analysis, introduced stochastic calculus into the study of finance.
Quantitative finance started in the U.S. in the 1930s as some astute investors began using mathematical formulae to price stocks and bonds.
Harry Markowitz's 1952 Ph.D thesis "Portfolio Selection" was one of the first papers to formally adapt mathematical concepts to finance. Markowitz formalized a notion of mean return and covariances for common stocks which allowed him to quantify the concept of "diversification" in a market. He showed how to compute the mean return and variance for a given portfolio and argued that investors should hold only those portfolios whose variance is minimal among all portfolios with a given mean return. Although the language of finance now involves Itō calculus, minimization of risk in a quantifiable manner underlies much of the modern theory.
In 1969 Robert Merton introduced stochastic calculus into the study of finance. Merton was motivated by the desire to understand how prices are set in financial markets, which is the classical economics question of "equilibrium," and in later papers he used the machinery of stochastic calculus to begin investigation of this issue.
At the same time as Merton's work and with Merton's assistance, Fischer Black and Myron Scholes were developing their option pricing formula, which led to winning the 1997 Nobel Prize in Economics. It provided a solution for a practical problem, that of finding a fair price for a European call option, i.e., the right to buy one share of a given stock at a specified price and time. Such options are frequently purchased by investors as a risk-hedging device. In 1981, Harrison and Pliska used the general theory of continuous-time stochastic processes to put the Black-Scholes option pricing formula on a solid theoretical basis, and as a result, showed how to price numerous other "derivative" securities.
[edit] Education
Quants often come from physics or mathematics backgrounds rather than finance related fields, and quants are a major source of employment for people with physics and mathematics Ph.D's. Typically, a quant will also need extensive skills in computer programming.
This demand for quants has led to the creation of specialized Masters and PhD courses in mathematical finance, computational finance, and/or financial reinsurance. In particular, Masters degrees in financial engineering and financial analysis are becoming more popular with students and with employers. London's Cass Business School was the pioneer of quantitative finance programs in Europe, with its MSc Quantitative Finance as well as the MSc Financial Mathematics and MSc Mathematical Trading and Finance programs providing some leading global research. Carnegie Mellon's Tepper School of Business, which created the Masters degree in financial engineering, reported a 21% increase in applicants to their MS in Computational Finance program, which is on top of a 48% increase in the year before.[1][when?] These Masters level programs are generally one year in length and more focused than the broader MBA degree.
[edit] Front Office Quant
Within Banking, quants are employed to support trading and sales functions. At the very simple level Banks buy and sell investment products known as Stocks (Equity) and Bonds (Debt). They can gain a good idea of a fair price to charge for these because they are liquid instruments (many people are buying and selling them) and thus they are governed by the market principles of supply and demand – the lower your price the more people will buy from you, the higher your price the more people will sell to you. Over the last 30 years a massive industry in derivative securities has developed as the risk preferences and profiles of customers have matured. The idiosyncratic, customised nature of many of these products can make them relatively illiquid and hence there are no handy market prices available. The products are managed, that is, actualised, priced and hedged, by means of financial models. The models are implemented as software and then embedded in front-office risk management systems. The role of the quant is to develop these models.
[edit] Mathematical and statistical approaches
According to Fund of Funds analyst Fred Gehm, "There are two types of quantitative analysis and, therefore, two types of quants. One type works primarily with mathematical models and the other primarily with statistical models. While there is no logical reason why one person can't do both kinds of work, this doesn’t seem to happen, perhaps because these types demand different skill sets and, much more important, different psychologies.[2]"
A typical problem for a numerically oriented quantitative analyst would be to develop a model for pricing and managing a complex derivative product.
A typical problem for statistically oriented quantitative analyst would be to develop a model for deciding which stocks are relatively expensive and which stocks are relatively cheap. The model might include a company's book value to price ratio, its trailing earnings to price ratio and other accounting factors. An investment manager might implement this analysis by buying the underpriced stocks, selling the overpriced stocks or both.
One of the principal mathematical tools of quantitative finance is stochastic calculus.
According to a July 2008 Aite Group report, today quants often use alpha generation platforms to help them develop financial models. These software solutions enable quants to centralize and streamline the alpha generation process.[3]
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