# Using moments from annual data to calibrate a quarterly model

Hello,

I have annual data of GDP deviations from a trend, expressed in percent of trend GDP. I would like to use this data to calibrate shocks in a quarterly model (unfortunately I can’t re-calibrate the model to be in annual frequency as well). In particular, I would need to calibrate the shock’s standard deviation and its AR(1) coefficient.

Regarding the standard deviation, my understanding is that I just need to calibrate the shock such that the resulting (quarterly) standard deviation of GDP in the model (expressed in percent of steady state output) equals the (annual) standard deviation in the data. I suspects this works because the for this type of variable, the correct way to aggregate quarterly moments into annual moments is just to take an average
( this is how I would understand p. 4232 of Born and Pfeifer, https://pubs.aeaweb.org/doi/pdfplus/10.1257/aer.104.12.4231 ).

Does this approach sound reasonable to you? And, furthermore, does somebody have an idea how I could use my data to calibrate the AR(1) coefficient of my shock? Intuitively, a given AR(1) parameter implies a higher persistence in annual than in quarterly data. Does someone know how to go about this?

Many many thanks for any help!
Simon

You need to be careful. The averaging in our paper refers to the percentage deviations from trend, i.e. the mean. But you are interested in the standard deviations, which depend on the covariances. Given that you have an AR-process, these are not 0 and you outlined approach will fail.
You could work out the formulas analytically, but my experience is that it is often quicker to simply simulate the process.
What are your targets for the annual standard deviation and the autocorrelation in annual data?