Question: Consider the first-order autoregressive model ???????? = ????0 + ????????????1 + ????????, where the constant ????0 is a function of the mean of the series.

Consider the first-order autoregressive model ???????? = ????0 + ????????????−1 + ????????, where the constant ????0 is a function of the mean of the series.

(a) Derive the autocovariances ???????? = ????([???????? − ????][????????−???? − ????]) for this series.

(b) Calculate and plot the autocorrelation function for ???? = 0.8 using the R command ARMAacf(); see help(ARMAacf) for details.

(c) Calculate and plot the partial autocorrelation function for the same process.

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