(a) Why is it important to factorize the autoregressive and moving average operators after fitting a model to an observed series?

(b) It was shown by Jenkins (1975) that the number of mink skins ???????? traded annually between 1848 and 1909 in North Canada is adequately represented by the AR(4)

model

(1 − 0.82???? + 0.22????2 + 0.28????4)[ln(????????) − ????] = ????????

Factorize the autoregressive operator and explain what the factors reveal about the autocorrelation function and the underlying nature of the mink series. The data for the period 1850--1911 are listed as Series N in Part Five of this book. Note that the roots of ????(????)=0 can be calculated using the R commond polyroot(), where the autoregressive parameters are entered with their signs reversed; see help(polyroot)

for details.