The RATS Software Forum

Dear Tom,

I have question concerning the examples for low pass filters in the textbook examples of Brockwell and Davies, second edition. File itsf2p25.rpf deals with an equal weighted centered moving average over 2q+1 periods, 5 years in the example. From some other textbooks i have learned that the length of a moving average is half the cycle length of the smoothed series, usually demonstrated with a sine wave example. In the Brockwell and Davis example, that would be a 10 year cycle.

In the file itsf2p28.rpf, the code for exponential and frequency smoothing is provided. In know there is a formula to calculate alpha as an approximation to the periods of a simple moving average. For the frequency smoothing, a procedure @freqsmoth is provided with an option frequency. The real number in the example is 0.4 and implies that 40 percent of half the nords around the center will be excluded. My question is, whether there is a formula for the value to provide in the frequency option, which approximated the 2q+1 in the example for the simple moving average?

Best regards
PeterF

Usually you want to analyze that in the other direction---the bandpass filter is what you want (theoretically), but it is an infinite two-sided lag filter with slowly declining tails, so you want a finite lag filter which provides similar properties. (Baxter-King and Christiano-Fitzgerald being two examples in the economics literature).

Dear Tom,

thank you for the quick reply.

Best regards
PeterF