Metode ARIMA Box-Jenkins

Model ARIMA Box-Jenkins Model ARIMA Box-Jenkins Identification of STATIONER TIME SERIES Estimation of ARIMA model Diagnostic Check of ARIMA model Forecasting

Estimation and Testing parameter ARIMA model

t-values and prob-values for testing parameter model ARIMA

Parameters ARIMA

model estimates

Diagnostic Checking of ARIMA model … [white noise residual]

Ljung-Box statistic for testing white noise residual

ACF of residual

Forecasting of ARIMA(p,d,q) model

Forecasting of AR(1) model

or

Forecasting of MA(1) model Forecasting of MA(1) model

Example: Daily readings of viscosity of Chemical Product XB-77-5 [Bowerman and O’Connell, pg. 471]

Example: IDENTIFICATION step [stationary, ACF and PACF]

ACF PACF

Stationer time series

Dies down [sinusoidal] Cuts off after lag 2

Example: ESTIMATION and DIAGNOSTIC CHECK step

Estimationand Testingparameter

Diagnostic Check (white

noise residual)

Example: DIAGNOSTIC CHECK step … [Normality test of residuals]

Example: FORECASTING step [MINITAB output]

Calculation: FORECASTING (FITS and FORECAST) [continued]

MINITAB command: IDENTIFICATION Step

Plot DataPlot Data stationarity data

ACF & PACF data to find tentative

ARIMA model

IDENTIFICATION Step: Time Series Plot …

IDENTIFICATION Step: ACF data …

IDENTIFICATION Step: PACF data …

MINITAB command: ESTIMATION, DIAGNOSTIC CHECK & FORECASTING Step

Estimation, Diagnostic Check and Forecasting

MINITAB command: Normality test for residual