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I have a time series data that used quarterly information on a variable, but has now shifted to bi-monthly releases, from September 2008 to July 2021. This is a survey based measure, released at the end of each quarter/ two months.

But slowly they changed the timings of release.

It evolved like this:

Round1 Round2 Round3 Round4 Round5 Round6 From-To
September December March June Sep 2008 - Jun 2016
September November December March May June Sep 2016 - Jun 2018
September November January March May July Sept 2018 - July 2021

There are 2 issues:

  1. This isn't of uniform frequency. It was quarterly from Sep 2008 to 2016, then became bimonthly.

  2. Even after becoming bi-monthly, it's release dates have changed. From Sep 2016 - Jun 2018, the gap between subsequent releases wasn't constant. This was corrected from 2018, with a constant gap of 2 months between releases.

If I want to fit an ARIMA model on this time-series, how should I deal with these issues?

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If you insist on using some standard time series model this will be problematic as standard time series models such as ARIMA require fixed frequency.

There are some possible ways of dealing with this:

  1. You could try to aggregate all data on quarterly frequency. I can see that this might be somewhat more problematic due to uneven gaps on the bimonthly frequency, but you could just fit some spline through to data to estimate what the values of quarter would be. This will lead to loss of some information but to me it seems as the most straightforward way of approaching the issue.
  2. You could simply intrapolate the missing data, and thus covert the earlier quarterly data to bimonthly, although, this would produce artificially smoothed series and most of your data would intrapolated which would be problematic.

Alternatively, instead of using simple time series models you could use models that allow for non-fixed frequency. An overview of such models can be found in Casals et al 2005.

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