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I have four time series that cover the same time period. I want to perform cointegration analysis on them to investigate any potential cointegration relations and to estimate a VECM model. However, two of the series are monthly data and two are yearly data. I suppose that leaves me two options: interpolate the yearly data to monthly data or aggregate the monthly data to yearly data.

This raises two questions:

  1. Which of these two options is preferred? I'm leaning towards aggregation, because I feel that throwing away information is more statistically sound than interpolating, which forces some structure into the data to fill the gaps.
  2. What is the best way to perform the preferred method of 1? That is, if I should interpolate, what is the best way to do so? Linear interpolation? Exponential? Cubic splines? Constant? Or if I should aggregate: should I take the arithmetic mean? Geometric mean? Value of January? Or something else perhaps?

Thanks in advance.

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