Let yt be a seasonal process such that yt = (1 + 0.2B)(1 − 0.8B12)_t, where __ = 1. (a) Find the coefficients _j of the AR(_) expansion of the process. (b) Plot the theoretical ACF of yt. (c) Plot the...

Let
y
t
be a seasonal process such that
y
t
= (1 + 0.2B)(1
−

0.8B12)_
t,

where
_
_
= 1.

(a) Find the coefficients
_
j
of the AR(_) expansion of the process.

(b) Plot the theoretical ACF of
y
t.

(c) Plot the theoretical PACF of this process.

(d) Find the spectral density of this process and plotted it.

Let fxtg be the seasonal process

(1 􀀀 0:7B2)xt = (1 + 􀀀:3B2)zt;

where fztg is WN (0; 1).

(a) Find the coe_cients f jg of the representation xt =

P1 j=0 jzt􀀀j .

(b) Find and plot the _rst _ve components of the ACF of the process

fxtg.

(c) Simulate 400 observations from this model. Plot the series and calculate

the ACF and PACF.

(d) Based on the previous question, estimate the parameters of the simulated

series via maximum likelihood estimation.