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I am interested in financial time series and I have a small question regarding the use of the forecast package.

The time series I am interested in is a monthly one and present clear evidences of seasonality. Thus there is a need to use a lag 12 differentiation. After this step, I apply a full collection of KPSS and ADF tests on the resulting time series and the conclusion is that it is stationnary up to a linear trend.

However if I perform those tests before applying the lag 12 diff operator, the conclusion is that the time series is not stationnary and needs to be differentiated.

Here are my questions:

1) Is it better checking the stationnarity through the tests before or after differentiating at lag 12 ?

2) If it is better (as I do for the moment) to differentiate at lag 12 priorly, what should I do if the outcomes of the tests are that the resulting time series is stationnary up to a linear trend ? I guess I cannot simply use auto.arima with D=1 and xreg=1:N since the linear regression would then be done before differentiating at lag 12.

Thanks.

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