Using a normal random number generator, generate 100 observations of the following series, plot and discuss the di_erences. (a) AR(1), _ = 0:6 (b) MA(1), _ = 􀀀0:6 (c) ARMA(1,1) con _ = 0:6 and _ =...

Using a normal random number generator, generate 100 observations

of the following series, plot and discuss the di_erences.

(a) AR(1), _ = 0:6

(b) MA(1), _ = 􀀀0:6

(c) ARMA(1,1) con _ = 0:6 and _ = 􀀀0:6

Consider a series modeled by the following process:

(1 􀀀 0:82B + 0:22B2 + 0:28B4)[log(z) 􀀀 ] = "t;

where "t is white noise sequence.

(a) Factorize the autoregressive operator, and explain the aspects that

the factorization reveals regarding the autocorrelation function and

the periodic components of this series.

(b) What is the formula which allows the forecasting of this series?