Dear Johannes,
Thank you very much for your helpful guidance, I am grateful.
I have formulated multiple DSGE model for robustness analysis, each model specification is a little different to the other DSGE models, and they are Not nested model.
However, then I simulate these DSGE models to get observable variables, then calculate business cycle statistics in terms of standard deviations, autocorrelations, correlation with output, etc, so as to compare among these models and between models and data.
My question is, assume rhoA is autocorrelation calculated from a simulated observable variable of model A, and rhoB is autocorrelation calculated from a simulated observable variable of model B, sdA is standard deviation calculated from a simulated observable variable of model A, and sdB is standard deviation calculated from a simulated observable variable of model B. if rhoA is greater than rhoB, do we expect sdA to be smaller than sdB? because if the simulated variable is more autocorrelated , it should have a smaller standard deviation?
Thank you very much and look forward to hearing from you.
Best regards,
Jesse
The standard deviation of an AR(1) process is \sigma_e/(1-\rho^2) , where \sigma_e is the standard deviation of the shock. If the simulated observables have the same standard deviation (a big if), then if the autocorrelations differ, the standard deviations of the shock must be different as well.