# Frequency decomposition of forecast error variance

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?

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

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