My Experience in ARIMA

Minitab Project Report

I would like to share my experience in using one of the tool in minitab to do a forecast based on historical data which is called ARIMA . Whoever reads this article, please feel free to comment or correct the steps I highlighted if you think you have a better way to do ARIMA in minitab.

Steps of ARIMA

(1) Check data stationary .

If yes proceed with ARIMA

If no need to do LOG transform ( for variance ) and DIFFERENCE ( for mean )

How can you know you data is stationary of not ?

• Graph data (raw & transformed)
• No evidence of change in the mean over time - Mean stationary
• No evidence of change in the variance over time -
  Variance stationary
• The Autocorrelation Plot (ACF) can expose non-stationary

Autocorrerlation of stationary data drops to zero relatively quickly, while for a non-stationary series they are significantly differently from zero for several lags

Example :

Actual data and transformed of Actual data showed :

No evidence of change in the mean over time

No evidence of change in the variance over time

AND Autocorrelation result also showed data drops to zero relatively quickly :

Thus above “ACTUAL” data considered as STATIONARY data .

(2) Model Selection

Examine data : Any seasonal or trend .( Use Autocorrelation , Partial Auto Correlation )

Example :

Above “ACTUAL” data can be concluded no TREND and SEASONAL .

Below data can be concluded as having TREND and SEASONAL .

Autocorrelation result showed a LAG :

This is the example of Non - Stationary data with seasonal .( This example taken from Six Sigma Academy )

For this type of data , need to do DIFFRENCE to make it STATIONARY before proceeding with ARIMA .

After doing some DIFFERENCE below will be the result of Autocorrelation :

As you can see , the autocorrelation from the DIFFERENCE data , reduce to ZERO , same as the result from the autocorrelation for ACTUAL data above .

Remark : DIFFERENCE is a funtion in minitab at STAT -> TIME SERIES -> DIFFERENCES

(3) Estimation Of Parameters

During the selection of ARIMA model , there are some guidelines to select the value for

p ( relates with AutoRegressive) , d ( relate with Intergrated ) , q ( relate with Moving Average ).

But in general there are 5 basics ARIMA ( AutoRegressive Intergrated Moving Average ) , which are

(p,d,q) = (1,1,0) / (0,1,1) / (1,1,1) / (0,1,2) / (2,1,0)

Once your data satsified the criteria ( STATIONARY DATA ) to be analyzed with ARIMA , you can try each of the model and judge models that fit with your data based on calculated p-value as below example :

Among the 5 models , only model ( 1,1,0 ) and (0,1,2) indicated p-value < 0.05 which is significant to the data. Thus we can do forecast from our data by using these 2 parameters and which of these 2 that is more reprentative can be selected based on process kowledge and experience .