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I am trying to estimate a regression with variables of different periodicity. The dependent variable is given monthly, whereas most other independent variables are also given monthly, but some are given yearly and others are given quarterly.

A typical approach to solve this is just to copy the yearly variables $12\times$ and the quarterly ones $4\times$.

But this doesn't seem right, as for example in case of a yearly explanatory variable, only the dependent monthly variable varies over 12 observations, while the yearly variable stays constant.

It seems to me the effect of the yearly variable on the monthly one cannot be measured this way properly, as within a single year, we cannot observe an effect at all. On the other hand, the yearly variables cannot be updated more often than yearly, and e.g. division by 12 doesn't seem to be any better.

So I know of different approaches to disaggregate or to aggregate data from one frequency to another, but my question is more what are the effects on regression analysis? Does it still make sense if I e.g. copy yearly variables by 12 in a monthly setting if I got plenty of years? Also note that I got many observations over time and cross-sectionally (i.e. a panel format), but from my perspective the issue can be illustrated already by looking at one unit over time.

Some data in R to illustrate this:

set.seed(1)
test <- data.frame(growth = rnorm(240),time=c(seq(as.Date("1988/02/01"),as.Date("2008/01/31"), "month")-1),
ylyvar=unlist(sapply(1:20,function(x) rep(sample((x*100)*1000,size = 1),12),simplify = F)),
qlyvar = unlist(sapply(1:80,function(x) rep(sample((x)*1000,size = 1),3),simplify = F)),
depvar1=rnorm(240),
depvar2=rnorm(240))
Talik3233
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  • I think I can see what you're talking about but if not a snippet of the tables you're using could be useful. If you're comparing to a yearly figure or a quarterly figure can't you roll your data up for that year or quarter rather than spread your yearly variable out and generalise it over the whole year? – Lio Elbammalf Feb 25 '19 at 15:43
  • I suggest a test where the monthly values and monthly equivalent values are used to determine the best regression analysis you can make with the data you have. – James Phillips Feb 25 '19 at 15:45
  • Thanks for the comments. @LioElbammalf I added some sample data to illustrate my setup. – Talik3233 Feb 25 '19 at 16:02
  • Have you considered over time disaggregation methods like Chow Lin with modifications (check the function td()): https://cran.r-project.org/web/packages/tempdisagg/tempdisagg.pdf The methods are really worth considering. The impact of disaggregation exists, as you do not recover the full picture unless you work with slow varying data like population statistics. Another idea could be trying state space methods, where lower frequency data would be treated as the data with periodically missing observations. – Dmitrij Celov Feb 26 '19 at 14:25

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