How can we render a daily time series into a monthly series while retaining the effect of extreme values in the series?

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John C Frain

There are several ways to convert a daily series into a monthly one. Popular methods include

Taking the average (arithmetic or geometric).

Taking the value at the end of the month

Taking the value at the middle of the month.

Taking the value at the beginning of the month.

Taking the maximum of the series in a month,

Take the minimum of the series in a month, or

the difference between that maximum and minimum.

Get an estimate of the monthly variance of the series

What you do now depends on the nature of your monthly variable and the process you are trying to capture. Look at the economics or finance of the process. For example, if you think that your monthly variable is dependent on the volatility and level of your daily series, you might consider using one of 1 to 4 for the level and 7 or 8 for the volatility. There are many combinations that might be useful but that is up to you. It may also be necessary to log transform your variables before analysis.

Chbili Sfia

John C Frain in my study i try to convert one serie, (which is daily serie), to monthly serie, but in same time i want to reserve the effect of large variations in the new monthly serie, i tried to do that using arithmetic average, but the extrême variations seem to be neglected. I’ll test the other methods that you cited.

thank you very much for your explanations .

Masoud Ataei yes, I tried with Harmonic and Contra-harmonic Means, I got the same results with a very small difference in both cases, the new monthly serie seems to show the extreme variations effects

it was very helpfull, thank you very much.

Gyehong Kim

Eric Ghysels (unc.edu)

MIDAS model might help.

Saheed Busayo Akanni

The conversion of daily time series into monthly can be easily done using any of the time series econometrics packages like the Eviews, Gretl, R, etc depending on your choice of package. But I will advise that you carryout the conversion in R using either xts function or the following codes:

data_monthly