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:
- 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.
- 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.