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I have a problem in multivariate time series. The data consist of three time series related to foreign trade. Although my client is still doing research and attempting to find monthly data for all three series, she may only have quarterly data for some series. She has data for 10 years.

I am considering interpolating monthly data from the quarterly data, and was wondering if this is a good approach, and what any drawbacks there are.

Thanks

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    $\begingroup$ What can you tell us about the signal? Surely it must have some properties or constraints we can leverage to obtain a better estimate. $\endgroup$ – Emre May 14 '12 at 18:32
  • $\begingroup$ The signal is going to be something about the relationship between China and the United States and their mutual trade. $\endgroup$ – Peter Flom May 14 '12 at 18:34
  • $\begingroup$ How do you intend to impute monthly from quarterly? I may not be thinking straight but I don't see how you can impute your way into a finer scale of resolution. $\endgroup$ – Macro May 14 '12 at 18:40
  • $\begingroup$ Interpolate .... the simplest way would be linear. So if, say, at Q1 the value is 100 and at Q2 it's 200, we say Month1 = 100, Month4 = 200, so month2 = 133 and month3 = 167. It's clearly an assumption, but I am not sure how much or what sort of problem it causes for time series modeling. $\endgroup$ – Peter Flom May 14 '12 at 18:46
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    $\begingroup$ I would add that if you have high frequency oscillations it could be that 2 months should be high and one month low or vice versa. So linear interpolation could impute poorly to all three months. You need to knwo something about what you don't know to do this right. You are probably making unverifiable assumptions. If yuo are lucky and the assumptions are approximately right you win. If not yuo can lose badly! $\endgroup$ – Michael Chernick May 14 '12 at 22:14
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If you have monthly series that are related to the series you want to interpolate, you can use the Chow-Lin regression based interpolation method. This method, along with other univariate and multivariate procedures, have been implemented in the software Ecotrim, which can be downloaded here.

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    $\begingroup$ +1 The abstract makes it sound like one-dimensional cokriging (which would be a good approach, too). $\endgroup$ – whuber May 15 '12 at 20:56

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