Consider a stationary AR(2) process:(adsbygoogle = window.adsbygoogle || []).push({});

X_{t}- X_{t-1}+ 0.3X_{t-2}= 6 + a_{t}

where {a_{t}} is white noise with mean 0 and variance 1.

Find the partial autocorrelation function (PACF).

I searched a number of time series textbooks, but all of them only described how to find the PACF for an ARMA processwith mean 0(i.e. without the constant term). So if the constant term "6" above wasn't there, then I know how to find the PACF, but how about the case WITH the constant term "6" as shown above?

I'mguessingthat (i) and (ii) below would have the same PACF, but I'm just not so sure. So do they have the same PACF? Can someone explain why?

(i) X_{t}- X_{t-1}+ 0.3X_{t-2}= 6 + a_{t}

(ii) X_{t}- X_{t-1}+ 0.3X_{t-2}= a_{t}

Any help would be much appreciated! :)

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# Time Series: Partial Autocorrelation Function (PACF)

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