Knowing whether a time-series has been differenced appropriately in order to make it stationary

May 7, 2010

(This article was first published on Econometrics_Help, and kindly contributed to R-bloggers)

Hello everybody,

Today I would like to make you learn a simple method (and of-course using R) how to identify whether a time-series has been differenced appropriately while making it stationary.

Suppose, you have made a series stationary by differencing it, now in order to know whether it is neither over nor under differenced subject the current series against next level differenced series either using a Regression or ARIMA having Constant/Intercept. Next, from the results obtained gather either Akaike-Information-Criterion value (AIC) or Root-Mean-Squared value (RMSE), if AIC (or RMSE) value from current series is lower than next level differenced series than one can conclude that current series is appropriately differenced to make it stationary.

In R, it can be done by scripting following two commands:
arima(“series to be test”,c(0,0,0));  # first current series with constant)
arima(“series to be test”,c(0,1,0));  # next level differencing or one more lag difference of the current series with

In SAS, it can be identified by using IACF plots of PROC ARIMA.

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