PERAMALAN DATA TIME SERIES

Transkripsi

1 PERAMALAN DATA TIME SERIES

2 DATA TIME SERIES Time series merupakan data yang diperoleh dan disusun berdasarkan urutan waktu atau data yang dikumpulkan dari waktu ke waktu. Waktu yang digunakan dapat berupa minggu, bulan, tahun dan sebagainya.

3 DATA TIME SERIES The rate variable is collected at equally spaced time periods, as is typical in most time series and forecasting applications. Many business applications of forecasting utilize daily, weekly, monthly, quarterly, or annual data. The data may be: Instantaneous, such as the viscosity of a chemical product at the point in time where it is measured; It may be cumulative, such as the total sales of a product during the month; or It may be a statistic that in some way reflects the activity of the variable during the time period, such as the daily closing price of a specific stock on the New York Stock Exchange.

4 CONTOH 1 Harga saham AAPL: 5 tahun, direkam dalam data per minggu

5 CONTOH 2

6 FORECAST

7 KEGIATAN PERAMALAN (FORECASTING) Merupakan bagian integral dari pengambilan keputusan. Mengurangi ketergantungan pada hal-hal yang belum pasti (intuitif). Ada saling ketergantungan antar divisi. Contoh, kesalahan proyeksi penjualan akan mempengaruhi ramalan anggaran, pengeluaran operasi, arus kas, persediaan, dst. Dua hal utama dalam proses peramalan yang akurat dan bermanfaat: Pengumpulan data yang relevan. Pemilihan teknik peramalan yang tepat.

8 FIELD OF FORECASTING The reason that forecasting is so important is that prediction of future events is a critical input into many types of planning and decision-making processes, with application to areas such as the following: Operation Management: Business organizations routinely use forecasts of product sales or demand for services in order to schedule production, control inventories, manage the supply chain, determine staffing requirements, and plan capacity Marketing: Forecasts of sales response to advertising expenditures, new promotions, or changes in pricing polices enable businesses to evaluate their effectiveness, determine whether goals are being met, and make adjustments.

9 Finance and Risk Management: Investors in financial assets are interested in forecasting the returns from their investments. Financial risk management requires forecasts of the volatility of asset returns so that the risks associated with investment portfolios can be evaluated Economics: Governments, fnancial institutions, and policy organizations require forecasts of major economic variables, such as gross domestic product, population growth, unemployment, interest rates, inflation, job growth, production, and consumption Industrial process control Demography

10 METODE PERAMALAN Terdapat dua pendekatan peramalan : Kualitatif Kuantitatif.

11 METODE PERAMALAN KUALITATIF Metode ini digunakan ketika data historis langka atau bahkan tidak tersedia sama sekali; Metode ini (biasanya) menggunakan opini dari para ahli untuk memprediksi kejadian secara subyektif; Contoh: penjualan dari produk baru, lingkungan dan teknologi di masa mendatang. Keuntungan: berguna ketika tidak ada data historis; Kelemahan: subyektif

12 GLAD YOU DIDN T SAY IT

13 METODE PERAMALAN KUANTITATIF Metode ini digunakan ketika tersedia data historis; Metode ini mengkonstruksi model peramalan dari data yang tersedia atau teori peramalan; Keuntungan: Obyektif Metode kuantitatif dibagi menjadi 2 jenis: time series dan causal

14 Metode peramalan causal Meliputi faktor-faktor yang berhubungan dengan variabel yang diprediksi seperti analisis regresi. Mengasumsikan bahwa satu atau lebih faktor (variabel independen) memprediksi masa datang. Input: variabel dependent dan independent Proses: hubungan sebab-akibat Output: model untuk meramalkan var dependen Metode Peramalan time series merupakan metode kuantitatif untuk menganalisis data masa lampau yang telah dikumpulkan secara teratur dengan menggunakan teknik yang tepat. Data historis digunakan untuk memprediksi masa datang Input: data historis Proses: pembangki tan proses Output: model untuk meramalkan data masa datang Hasilnya dapat dijadikan acuan untuk peramalan nilai di masa yang akan datang (Makridakis. S., 1999).

15 SYARAT-SYARAT PERAMALAN KUANTITATIF 1. Tersedia info pada waktu lalu 2. Info tersebut dapat dikuantitatifkan 3. Diasumsikan pola pada waktu-waktu lalu akan berlanjut di masa yang akan datang (assumption of constancy)

16 TIPE-TIPE METODE KUANTITATIF 1. Naif/intuitif y t 1 y t y t y t y t 1 Data mendatang = data sekarang + proporsi peningkatan 2. Formal Berdasarkan prinsip-prinsip statistik

17 KOMPONEN TIME SERIES Trend Cyclical Seasonal Random/ horisontal

18 KOMPONEN/POLA DATA Terdapat empat pola data yang lazim dalam peramalan: 1. Pola horisontal 2. Pola musiman 3. Pola siklis 4. Pola tren

19 HORISONTAL Pola horisontal: Terjadi bila mana data berfluktuasi di sekitar rata-ratanya.

20 MUSIMAN Pola musiman: Terjadi bila mana nilai data dipengaruhi oleh faktor musiman (misalnya kuartal tahun tertentu, bulanan atau mingguan). Menunjukkan puncak-puncak (peaks) dan lembah-lembah (valleys) yang berulang dalam interval yang konsisten.

21 SIKLIS Pola siklis. Terjadi bila mana datanya dipengaruhi oleh fluktuasi ekonomi jangka panjang seperti yang berhubungan dengan siklus bisnis. Pergerakan seperti gelombang yang lebih panjang daripada satu tahun. Belum tentu berulang pada interval waktu sama.

22 TREND Pola trend. Terjadi bila mana ada kecenderungan kenaikan atau penurunan dalam data.

23 SIMPLE AVERAGE We will first investigate some averaging methods, such as the "simple" average of all past data. Example. Seorang manager toko computer mempunyai data penjualan notebook perbulan. Dia mempunyai data 12 bulan penjualan sebagai berikut :

24 DATA Bulan Amount Bulan Amount The computed mean or average of the data = 10. The manager decides to use this as the estimate for next demand. Is this a good or bad estimate?

25 MSE We shall compute the "mean squared error": The "error" = true amount spent minus the estimated amount. The "error squared" is the error above, squared. The "SSE" is the sum of the squared errors. The "MSE" is the mean of the squared errors. The SSE = 36 and the MSE = 36/12 = 3.

26 KOMPUTASI Bulan $ Error Error Squared

27 MSE TERBAIK So how good was the estimator for the next demand? Let us compare the estimate (10) with the following estimates: 7, 9, and 12. Performing the same calculations we arrive at: Estimator SSE MSE

28 BUKTI ANALISIS Dapat dibuktikan secara matematis bahwa estimator yang meminimalkan MSE pada himpunan data random adalah mean. d Minimum MSE Y a 2 0 i da i 1 n

29 DATA WITH TREND Selanjutnya kita lihat data timeseries yang mengandung trend. Next we will examine the mean to see how well it predicts net income over time for data having a trend. The next table gives the income before taxes of a PC manufacturer between 1985 and 1994.

30 KOMPUTASI DATA Year $ (millions) Mean Error Squared Error

31 BUKTI EMPIRIS The question arises: can we use the mean to forecast income if we suspect a trend? A look at the graph below shows clearly that we should not do this.

32 Kasus di atas dapat diselesaikan antara lain dengan menggunakan regresi trend atau metode perataan yang lain seperti MA ganda, Metode Eksponensial Smoothing Linear Holt atau Brown.

33 FORECASTING PROCESS

34 DIAGRAM FORECASTING PROCESS

35 Problem definition: Understanding of how forecast will be used by customer The desired form of the forecast (e.g., are monthly forecasts required) Data collection: Obtaining the relevant history for the variable(s) that are to be forecast, including historical information The key here is relevant ; not all historical data are useful for the current problem Data analysis: Selection of the forecasting model to be used Time series plots of the data should be constructed and visually inspected for recognizable patterns, such as trends and seasonal or other cyclical components Model selection and fitting: Consists of choosing one or more forecasting models and fitting the model to the data By fitting, we mean estimating the unknown model parameters (OLS, optimization method)

36 Model validation: An evaluation of the forecasting model to determine how it is likely to perform in the intended application A widely used method for validating: data splitting, where the data are divided into two segments a fitting segment and a forecasting segment Forecasting model deployment: Involves getting the model and the resulting forecasts in use by the customer Monitoring forecasting model performance: Should be an ongoing activity after the model has been deployed to ensure that it is still performing satisfactorily

37 DATA FOR FORECASTING

38 EXTRACT Data extraction refers to obtaining data from internal sources and from external sources Such as third party vendors or government entities and financial service organizations

39 TRANSFORMATION transformation stage involves applying rules to prevent duplication of records and dealing with problems such as missing information. Sometimes we refer to the transformation activities as data cleaning Data cleaning is the process of examining data to detect potential errors, missing data, outliers or unusual values, or other inconsistencies and then correcting the errors or problems that are found.

40 LOAD Finally, the data are loaded into the data warehouse where they are available for modeling and analysis.

41 IMPUTATION Data imputation is the process of correcting missing data or replacing outliers with an estimation process. If the data does not have any specific trend or seasonal pattern Imputation replaces missing or erroneous values with a likely value based on other available information Mean value imputation consists of replacing a missing value with the sample average calculated from the non-missing observations. However, one must be careful if there are trends or seasonal patterns

42 IMPUTATION Stochastic mean value imputation: Consider the time series y 1, y 2,, y T and suppose that one observation y j is missing. We can impute the missing value as where k would be based on the seasonal variability in the data. It is usually chosen as some multiple of the smallest seasonal cycle in the data, example: 12 for monthly data.

43 IMPUTATION Regression imputation Is a variation of mean value imputation where the imputed value is computed from a model used to predict the missing value. The prediction model does not have to be a linear regression model.

44 REFERENCE