# Frequency change monthly series

I have a monthly series and I want to make it quarterly. I want to know which method I use. I used an arithmetic average but I do not trust these results. There is a procedure in Stata and Eviews I can use. Thanks in advance.

• What do your data represent? What is the purpose of making it a quarterly series? Why do you not trust the averages? – whuber Apr 29 '15 at 15:53
• My data are price index, and am creating a model where use of quarterly series. I do not trust the media, because I realized that when I calculate an average of these indexes, much of the variability observed in the monthly series, disappears in the quarterly series. I want the quarterly series, in the middle as possible, keep this variability presents the monthly series – albert Apr 30 '15 at 0:23
• Because the issue concerns the temporal support of your data, you need to explain what time this "price index" covers. Is it a monthly mean? The index at some time during the month, such as its middle or end? Perhaps its maximum or minimum value during the month? That will indicate the appropriate way to combine months into quarters. BTW, when you average things, variability typically does go down: that's a basic law of statistics. If your index represents some kind of average over the month, then it would be unrealistic to try to reproduce its variability in the quarterly version. – whuber Apr 30 '15 at 16:38

Quarterly price indices are going to vary less than monthly. In fact for price indices the default assumption is a square root rule for the variance of price returns, i.e. $\sigma_q^2=3\sigma_m^2$ for quarterly and monthly. It's almost never exactly square root, but the variance is certainly an decreasing function of the sampling frequency.

There are many ways to down sample price indices, but the most popular ones are: the simple average and the last price. I have seen people using max(), e.g. for VIX index. How you down sample depends on what is your objective really.

You should able to do what you want in R by setting the frequency to four if you are working with monthly data:

ts(tsobj, frequency = 4)

This is part of base R and spec.pgram()

Cheers

• It isn't clear that the OP uses R. In light of that, can you explain in software-neutral terms what you should do? – gung - Reinstate Monica Jul 30 '15 at 19:13
• Not only should you edit to explain the approach you're recommending, can you also explain how this approach can tell the difference between a monthly series that should be summed to produce a quarterly figure (e.g. flow-type variables, such as sales) and one like an index such as the OP has, which should not be summed? – Glen_b -Reinstate Monica Jul 30 '15 at 20:20