The Econometrics of Temporal Aggregation V - Testing for Normality

This post is one of a sequence of posts, the earlier members of which can be found here, here, here, and here. These posts are based on Giles (2014).

Some of the standard tests that we perform in econometrics can be affected by the level of aggregation of the data. Here, I'm concerned only with time-series data, and with temporal aggregation. I'm going to show you some preliminary results from work that I have in progress with Ryan Godwin. Although these results relate to just one test, our work covers a range of testing problems.

I'm not supplying the EViews program code that was used to obtain the results below - at least, not for now. That's because what I'm reporting is based on work in progress. Sorry!

As in the earlier posts, let's suppose that the aggregation is over "m" high-frequency periods. A lower case symbol will represent a high-frequency observation on a variable of interest; and an upper-case symbol will denote the aggregated series.

So,

               Y_t = y_t + y_{t - 1} + ......+ y_{t - m + 1} .

If we're aggregating monthly (flow) data to quarterly data, then m = 3. In the case of aggregation from quarterly to annual data, m = 4, etc.

Now, let's investigate how such aggregation affects the performance of the well-known Jarque-Bera (1987) (J-B) test for the normality of the errors in a regression model. I've discussed some of the limitations of this test in an earlier post, and you might find it helpful to look at that post (and this one) at this point. However, the J-B test is very widely used by econometricians, and it warrants some further consideration.

Consider the following small Monte Carlo experiment.