If W1;t = (1 􀀀 _1 B)"1;t and W2;t = (1 􀀀 _2 B)"2;t, where "1;t and "2;t are two independent white noise sequences, show that W3;t = W1;t+W2;t can be written as W3;t = (1 􀀀 _3 B)"3;t. Find...

If W1;t = (1 􀀀 _1 B)"1;t and W2;t = (1 􀀀 _2 B)"2;t, where "1;t and "2;t

are two independent white noise sequences, show that W3;t = W1;t+W2;t can

be written as W3;t = (1 􀀀 _3 B)"3;t. Find expressions for _3 and _2

3;t in terms

of the corresponding parameters of the other two processes.

Consider ARMA(1,1) process

yt = 10 + 0:8yt􀀀1 + "t 􀀀 0:5"t􀀀1

(a) Is this a stationary and an invertible process?

(b) Calculate the mean of yt.

(c) Calculate the autocovariance and autocorrelation functions.

(d) If possible, _nd the AR(1) and MA(1) representation.