(a) Suppose (left{w_{t} ight}) is a white noise with constant variance (sigma_{w}^{2}). What is the variance of the process (left{triangleleft(w_{t} ight) ight}) ? Why is

(a) Suppose \(\left\{w_{t}\right\}\) is a white noise with constant variance \(\sigma_{w}^{2}\). What is the variance of the process \(\left\{\triangle\left(w_{t}\right)\right\}\) ?

Why is this so?

(b) Generate 100 realizations of a white noise sequence with a variance of 1 .

Compute the variance of your sample \(w\) and the variance of \(\operatorname{diff}(\mathrm{w})\).

(c) Generate three bivariate white noise sequences of 100 realizations each.
Let the variance of the first of the bivariate variables be 1 and let the variance of the second be 2 in all three processes. For the first series, let the correlation between the two elements be 0.5 ; for the second, let the correlation be 0.0 ; and for the third, let the correlation be -0.5 .
Plot each bivariate time series on a separate graph (three graphs in all). In each graph use different line types or colors for the two terms in each time series.