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I think my question concerns statistical signal processing. I was referred to this site by a user at Cross Validated. I want to do a frequency-domain decomposition of generalized forecast error variance (GFEVD) from a bivariate and trivariate vector autoregression model (VAR) of exchange rates and inflation rates. I think I got a bit bogged down in the process. Given that I am sampling with a monthly frequency (I have monthly data), I think the maximum detectable frequency responses are bimonthly or once every two months. For example, frequencies from $\pi/2$ to $\pi$ should correspond to response times of roughly two to eight months. Am I overthinking it or am I right?

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  • $\begingroup$ Seems right by nyquist, yes $\endgroup$
    – Jdip
    Commented Apr 4 at 23:03
  • $\begingroup$ @Jdip Okay, thank you. $\endgroup$ Commented Apr 5 at 17:42

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The OP almost has it correct. Yes, if the time data is sampled at once/month, the unique frequency range for real data is from $f=0$ to $f=0.5$ cycles/month, or 1 cycle/2 months as the OP has written. However frequencies given as $\pi/2$ to $\pi$, assuming they correspond to normalized radian frequency which are in units of radians/sample, would correspond exactly to frequencies 0.25 cycle/month up to 0.5 cycles/month. This is 1 cycle every 4 months up to 1 cycle every 2 months.

The graphic below depicts the different units typically used for the frequency domain in a sampled system:

sampling units

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  • $\begingroup$ Thank you. Why didn't I realize $\pi/2$ corresponds to 1/4 of a cycle? It's obvious now you've said it. $\endgroup$ Commented Apr 8 at 10:12

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