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My problem is the following:

I have a model forecasting the sales of a certain brand. In period 4 a strike caused the sales to decrease. I want to know whether this strike has caused the sales to decrease permanently.

What I first thought to do is to split up the sample in a pre-strike period and post-strike period. If then the pre-strike period is stationary and the post-strike period has a unit-root, the effect is permanent (in the presence of a unit root, a shock will cause a long-term effect on the dependent variable). But according to Perron(1989) this procedure has low power.

Perron (1989) talks about a structural-break unit-root test. Does somebody know whether this test might solve my problem and if not, how I can possibly tackle this problem?

Many thanks in advance.

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  • $\begingroup$ 1) Splitting the sample in pre-strike and post-strike periods is a good idea to check the stability of the parameters in a model fitted to both subsamples. You could also apply the unit root test over overlapping subsamples of the same length or some other kind over subsamples of increasing size. This will require a relatively large sample, nonetheless. 2) The presence of a unit root is more a characteristic of the polynomial used to fit the data rather than a feature of the data themselves or a feature caused by an event such as a strike, but I don't know if that's what you imply. $\endgroup$ – javlacalle Dec 9 '14 at 8:40
  • $\begingroup$ Your question could probably be better addressed by intervention analysis rather than a unit root test. I recommend you this tag for your post. $\endgroup$ – javlacalle Dec 9 '14 at 8:41
  • $\begingroup$ You can checkout Zivot and Andrews test. Googling Zivot Andrews threw this overview (upo.es/RevMetCuant/art11.pdf) about unit root tests with structural breaks. It might be of interest. $\endgroup$ – mpiktas Dec 9 '14 at 12:49
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In the presence of a unit root, a shock will cause a long-term effect on the dependent variable does not imply If then the pre-strike period is stationary and the post-strike period has a unit-root, the effect is permanent.

A simple way to solve your problem (part of it was already suggested in the comments):

  1. Split the sample at the strike date into pre-strike and post-strike subsamples.
  2. Fit a time series model on the pre-strike subsample and another model for the post-strike subsample. (You could start from e.g. ARIMA model using function auto.arima() in package forecast in R.)
  3. From the models, obtain the means (with standard errors) for both periods.
  4. Compare the means using a t-test.

Why couldn't you just use a simple t-test for equality of the means in the two subsamples? Because the standard t-test requires the data points to be independent. Meanwhile, the data points in each subsample are most likely not independent of each other as your data is a time series.

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