A first-order autoregressive model is generated from the white noise series using the generating equations

A first-order autoregressive model is generated from the white noise series using the generating equations

4.5 (SS4.3) A first-order autoregressive model is generated from the white noise series using the generating equations where , for || < 1, is a parameter and the are independent random variables with mean zero and variance. (a) show that the power spectrum of is given by . (b) verify the autocovariance function of this process is , by showing that the inverse transform of is the spectrum derived in part (a). 1,="" is="" a="" parameter="" and="" the="" are="" independent="" random="" variables="" with="" mean="" zero="" and="" variance.="" (a)="" show="" that="" the="" power="" spectrum="" of="" is="" given="" by="" .="" (b)="" verify="" the="" autocovariance="" function="" of="" this="" process="" is="" ,="" by="" showing="" that="" the="" inverse="" transform="" of="" is="" the="" spectrum="" derived="" in="" part="">