A 25% drop in price may not have the same effect now as it had when the product was first introduced. Statisticians refer to this as time-varying parameters. Sometimes a promotion may not have the desired effect consistently thus an overall assessment might conclude that the promotion should be discontinued and declared as not having a statistically significant effect on sales.

Statisticians are concerned with validating the assumption that all of the data should be used to estimate parameters. Sometimes, we have too much data. The natural question is: Can we test for changes in parameters or model form over time allowing us to conclude that the most recent data should not be mixed or contaminated by using older data? (Chow's Test)

Consider the case of sales for the last 60 months and the knowledge that a promotion was put on at five points in time, viz. t=16,24,32,46 and 59 . Here we show a plot of the two series.

Standard regression modelling leads to the conclusion that the indicator variable, month of promotion, is not statistically significant.

However, if we employ a test to determine if the parameters of the model have changed over time, we find that there has been a significant change. The test results indicate that the first 31 observations should be treated independently from the last or more recent 29. This means that we have found a statistically significant difference in the parameters over time. The conclusion is that we should only use the most recent 29 observations.

Estimating the model using the most recent 29 values leads to a different conclusion with respect to the promotion variable.

If we closely examine the overall sales history and highlight the points of promotion, we can see these results. Notice how the first two points of promotion (t=16 and 24) show no apparent response while the opposite is true for t=32,46 and 59.

Statistical techniques are a very powerful way of discovering regularities, but one has to be constantly aware of the assumptions and use methodologies that aggressively test these assumptions.

The data.

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