PERAMALAN DATA TIME SERIES

DATA TIME SERIES

Time series merupakan data yang diperoleh dan disusun berdasarkanurutan 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, asis 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 belumpasti (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 atauteori 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.

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

Hasilnya dapat dijadikan acuan untuk peramalan nilai di masa yang akan datang (Makridakis. S., 1999).

Input: variabeldependent

danindependent

Proses: hubungan

sebab-akibat

Output: model untuk

meramalkanvar dependen

Input: data historis

Proses: pembangkitan proses

Output: model untuk meramalkandata masa datang

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 akandatang (assumption of constancy)

TIPE-TIPE METODE KUANTITATIF

1. Naif/intuitif

2. Formal• Berdasarkan prinsip-prinsip statistik

t

tt

tty

yyyy 1

1

Data mendatang = data sekarang + proporsi

peningkatan

KOMPONEN TIME SERIES

Trend

Seasonal

Cyclical

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 berulangdalam interval yang konsisten.

SIKLIS

Pola siklis. Terjadi bila mana datanya dipengaruhi oleh fluktuasi ekonomi jangkapanjang seperti yang berhubungan dengan siklus bisnis.

Pergerakan seperti gelombang yang lebih panjang daripada satu tahun. Belum tentuberulang pada interval waktu sama.

TREND

Pola trend. Terjadi bila mana ada kecenderungan kenaikan atau penurunan dalamdata.

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 penjualansebagai berikut :

DATABulan Amount Bulan Amount

1 9 7 11

2 8 8 7

3 9 9 13

4 12 10 9

5 9 11 11

6 12 12 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 $ Error Error Squared

1 9 -1 1

2 8 -2 4

3 9 -1 1

4 12 2 4

5 9 -1 1

6 12 2 4

7 11 1 1

8 7 -3 9

9 13 3 9

10 9 -1 1

11 11 1 1

12 10 0 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.

2

1

Minimum MSE 0n

i

i

dY a

da

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) Mean Error Squared Error

1985 46.163 48.776 -2.613 6.828

1986 46.998 48.776 -1.778 3.161

1987 47.816 48.776 -0.960 0.922

1988 48.311 48.776 -0.465 0.216

1989 48.758 48.776 -0.018 0.000

1990 49.164 48.776 0.388 0.151

1991 49.548 48.776 0.772 0.596

1992 48.915 48.776 1.139 1.297

1993 50.315 48.776 1.539 2.369

1994 50.768 48.776 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 menggunakanregresi trend atau metode perataan yang lain seperti MA ganda, Metode Eksponensial Smoothing Linear Holt atau Brown.

FORECASTING PROCESS

DIAGRAM FORECASTING PROCESS

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 theforecasting model to be used

• Time series plots of the data should be constructed and visually inspected for recognizable patterns, such as trendsand 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 estimatingthe unknown model parameters (OLS, optimization method)

Model validation:

• An evaluation of the forecasting modelto determine how it is likely to perform in the intended application

• A widely used method forvalidating: 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 ongoingactivity after the model has been deployed to ensure that it is still performing satisfactorily

DATA FOR FORECASTING

http://www.icidigital.com/blog/digital-marketing/migration-nothing-etl-extract-transform-load

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

TRANSFORMATION

transformation stage involves applying rules to prevent duplication of records and dealing with problems such as missinginformation.

Sometimes we refer to the transformation activities as datacleaning

Data cleaning is the process of examining data to detect potential errors, missing data, outliers or unusual values, or other inconsistencies and thencorrecting the errors or problems that are found.

LOAD

Finally, the data are loaded into the data warehouse where

they are available for modeling and analysis.

IMPUTATION

Data imputation is the process of correcting missing data or replacing outliers with an estimation process.

Imputation replaces missing or erroneous values with a “likely” value based on other available information

Mean value imputation consists of replacing a missing value withthe sample average calculated from the non-missing observations.

If the data does not have any specific trend or seasonal pattern

However, one must be careful if there are trends or seasonal patterns

IMPUTATION

Stochastic mean value imputation:

Consider the time series 𝑦1, 𝑦2, … , 𝑦𝑇 and suppose that one observation 𝑦𝑗 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.

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.

REFERENCE

https://onlinecourses.science.psu.edu/stat510/node/47