PERAMALAN DATA TIME SERIES
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.
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.
CONTOH 1 Harga saham AAPL: 5 tahun, direkam dalam data per minggu
http://finance.yahoo.com/quote/AAPL?ltr=1
CONTOH 2
http://kursdollar.net/
FORECAST
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.
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.
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
METODE PERAMALAN Terdapat dua pendekatan peramalan : Kualitatif Kuantitatif.
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
GLAD YOU DIDN’T SAY IT
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
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).
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)
TIPE-TIPE METODE KUANTITATIF 1. Naif/intuitif
yt 1
yt yt 1 yt yt
Data mendatang = data sekarang + proporsi peningkatan
2. Formal • Berdasarkan prinsip-prinsip statistik
KOMPONEN TIME SERIES Trend
Cyclical
Seasonal
Random/ horisontal
KOMPONEN/POLA DATA Terdapat empat pola data yang lazim dalam peramalan: 1. Pola horisontal
2. Pola musiman 3. Pola siklis 4. Pola tren
HORISONTAL Pola horisontal: Terjadi bila mana data berfluktuasi di sekitar rata-ratanya.
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.
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.
TREND Pola trend. Terjadi bila mana ada kecenderungan kenaikan atau penurunan dalam data.
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 :
DATA Bulan 1 2 3 4 5 6
Amount 9 8 9 12 9 12
Bulan 7 8 9 10 11 12
Amount 11 7 13 9 11 10
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?
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.
KOMPUTASI Bulan 1 2 3 4 5 6 7 8 9 10 11 12
$ 9 8 9 12 9 12 11 7 13 9 11 10
Error -1 -2 -1 2 -1 2 1 -3 3 -1 1 0
Error Squared 1 4 1 4 1 4 1 9 9 1 1 0
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
7
9
10
12
SSE
144
48
36
84
MSE
12
4
3
7
BUKTI ANALISIS Dapat dibuktikan secara matematis bahwa estimator yang meminimalkan MSE pada himpunan data random adalah mean.
d n 2 Minimum MSE Yi a 0 da i 1
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.
KOMPUTASI DATA Year $ (millions) 1985 46.163 1986 46.998 1987 47.816 1988 48.311 1989 48.758 1990 49.164 1991 49.548 1992 48.915 1993 50.315 1994 50.768
Mean 48.776 48.776 48.776 48.776 48.776 48.776 48.776 48.776 48.776 48.776
Error Squared Error -2.613 6.828 -1.778 3.161 -0.960 0.922 -0.465 0.216 -0.018 0.000 0.388 0.151 0.772 0.596 1.139 1.297 1.539 2.369 1.992 3.968
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.
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.
FORECASTING PROCESS
DIAGRAM FORECASTING PROCESS
Problem definition:
Data collection:
• Understanding of how forecast will be used by customer • The desired form of the forecast (e.g., are monthly forecasts required)
• 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:
Model selection and fitting:
• 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
• Consists of choosing one or more forecasting models and fitting the model to the data • By ftting, we mean estimating the unknown model parameters (OLS, optimization method)
Model validation:
Forecasting model deployment:
• 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
• 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
REFERENCE https://onlinecourses.science.psu.edu/stat510/node/47
