How to mix data with different time frequencies (monthly/quarterly)?

[Josh Bozeman]

I'm trying to mix 3 economic data sets from excel files (going to just copy and paste the data into the data editor probably)...two of the datasets are quarterly, but the third one is monthly. I need to run a vector auto regression on these, but how do I mix the quarterly with the monthly? Do I need to convert the one monthly data set to quarterly frequency by taking an average over the period or is there a simple way I'm missing?

I'm fairly new to stata and stats in general. I search the forums and see interpolation as an option for varying frequencies...not fully sure how to do that in stata, if that is the solution.

Thanks for any assistance.

[Andrew Musau]

Josh: You will probably need to convert the monthly data to quarterly data because you want all your data to have the same frequency. Depending on how your quarter is defined in the two datasets, e.g., quarter 1 runs from Jan1 - Mar 31, quarter 2, Apr1- Jun 30, etc., to convert the monthly data to quarterly data, take the observations corresponding to the end of March, the end of June, etc.

You should only average if your quarterly data (in the two datasets) is also averaged. Otherwise you introduce biases if you average the monthly data if the quarterly data represents the value of a variable at the beginning of a particular quarter.

[Nick Cox]

Whatever you do is manifestly dangerous, or at least fraught with difficulties. It's possible also to expand the quarterly data to monthly.

[Phil Bromiley]

I don't understand Nick's full concerns. Generally, I would think it makes much more sense to move from monthly data to quarterly than from quarterly to monthly. The sources that give us quarterly data sometimes create the quarterly data from monthly data. When you move from quarterly to monthly, you may be able to smooth or some such but monthly variation is simply not in the data.

If you know how the quarterly and monthly data were constructed and you can mimic the construction of the quarterly from the monthly data, I don't see why moving from monthly to quarterly would create any difficulties. For example, if the data are end-of-month values in both time series, then you should be able to get precisely parallel data to the quarterly from monthly by using the end of the right month. If both data are averages over the period, then averages of monthly data may not be precisely the same as the quarterly, but I'd think they would be very close.

If one is end of period and the other is averaged, you have problems of measurement error and the times may not align precisely. However, whether these are serious relative to the other noise in the data would depend on the data.

[Nick Cox]

I thought my note of caution was standard. If it seemed cryptic I should expand. Naturally "dangerous" is not danger in the sense of brain surgery, white-water rafting or whatever.

Whatever you do you're losing information (reduction to quarterly) or making implicit assumptions about the pattern of variation that are likely to be wrong and wrong to an extent that's difficult to analyse (converse).

Moving to quarterly also reduces your sample size by a factor of 3. "Sample size" is a slippery concept with time series, naturally, given serial dependence, etc. but most analyses I hear about here are pushing data very hard by trying to fit rather complicated models, so reducing dataset size is dangerous.

It's not axiomatic that averaging preserves information.

That's the nub of my comment.

Whether the difficulties rule out useful analyses is a different question. Even from a distance, it is clear that quarterly data allow a lot of helpful work.