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I have monthly shock series, which I want to convert to quarterly form. I have seen several methods like taking average of 3 months or summing 3 months for making a quarter. I would like to know how I can know which method is useful for me. Taking average or summing? Or is it something about personal choice in research methodology?

More details:

I intend to get impulse responses of real GDP to news shocks (which are already available). My GDP series are in quarterly form and my shock series in monthly form. So I need to convert shock series to quarterly form and do local projections.

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    $\begingroup$ Hi, could you please provide a bit more details and clarity in your Q about the problem? This will be different for different variables. If we are talking about total units of good Q produced by company X summing then would be appropriate, if we are talking about growth it would be more appropriate to do average and so on... choice on how to aggregate data is not a la carte but it depends on situation and context $\endgroup$ – 1muflon1♦ Apr 4 at 20:36
  • $\begingroup$ @1muflon1 Thanks. I have edited my question. $\endgroup$ – festakonik Apr 4 at 20:48
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I've seen them summed somewhere but I cannot exactly remember where. Ultimately I don't think that it makes much difference. The quarterly sum is just the average multiplied by three. Since local projections are just a bunch of OLS - one for each horizon, this is how you can think about the issue:

If $y_{t+h} = \alpha^h + \beta_h news\_shock_t + \sum_{j=1}^{L}\delta_j^hx_{t-j} + \dots + \sum_{j=1}^{L}\gamma_j^hy_{t-j} + \epsilon^h$ is the OLS for the h-th horizon, adding the shocks up is going to yield a $\beta_h$ that is exactly three times smaller than the $\beta_h$ you will obtain by averaging. The statistical significance will not be affected.

Since the units of the news shock most likely don't have any particular meaning both regressions yield exactly the same information.

A different approach instead of aggregating the news shocks up is to use industrial production data, which is usually available on monthly basis to disaggregate the GDP series down to monthly levels using Chow-Lin interpolation. A recent paper using this method would be Anaya et. al..

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