Using Quarterly Data in X-13ARIMA-SEATS

The latest U.S. Census seasonal adjustment program, the X-13ARIMA-SEATS, supports monthly, quarterly, and annual datasets. Although monthly and annual data samplings are definite, quarterly reporting can be more ambiguous. Which quarterly cycle are we talking about? Is it a Mar-Jun-Sep-Dec cycle, or something else?

This article was inspired by an inquiry from one of our customers: specifically, an Australian analyst using quarterly data following a Feb-May-Aug-Nov cycle. Is this a problem?

The U.S. Census X-13ARIMA-SEATS documentation assumes that quarterly data follows the Mar-Jun-Sep-Dec cycle. So, what can we do to adjust to the analyst’s situation?

If we were to ignore the reporting month discrepancy and use the data as is, then the calendar (trading days, leap year) and holidays adjustment would be incorrect for many periods. This would lead to errors.

If you don’t care for the prior data adjustment or wish to include a regression component in the forecast SARIMA model, then you could simply shift the date component in your dataset by one month so that it matches the Mar-Jun-Sep-Dec Cycle.

What is the alternative? We could resample, as follows:

  1. For stock-type data, we interpolate the levels on the Mar-Jun-Sep-Dec months.
  2. For flow-type data: (1) convert (i.e., aggregate) it to form a stock-type time series, (2) interpolate the stock-levels on the Mar-Jun-Sep-Dec months, and finally, (3) difference the interpolated values time series to reconstruct a flow-type.
NumXL comes with a simple, yet powerful, interpolation function – NxINTRPL(.), which allows you to interpolate the whole time series in one call. See the attached examples.

But what about the outputs: seasonally adjusted and forecast values?

X-13ARIMA generates all its outputs using the Mar-Jun-Sep-Dec cycle, so if you wish to take them back to a raw data quarter-cycle, you’ll need to carry on an interpolation for the new months.



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