Use the matrices of Problem 1 and the following command

to generate 200 observations from the VMA(1) model, \(\boldsymbol{z}_{t}=\boldsymbol{a}_{t}-\boldsymbol{C} \boldsymbol{a}_{t-1}\), where \(\boldsymbol{a}_{t}\) are iid \(N(\mathbf{0}, \boldsymbol{S})\).

- Plot the time series \(z_{t}\).

- Obtain the first two lags of sample CCMs of \(z_{t}\).

- Test \(H_{0}: \boldsymbol{ho}_{1}=\cdots=\boldsymbol{ho}_{5}=\mathbf{0}\) versus \(H_{a}: \boldsymbol{ho}_{i} eq \mathbf{0}\) for some \(i \in\{1, \ldots, 5\}\). Draw the conclusion using the 5\% significance level.

m2 = VARMAsim (200, malags = c(1), theta = C, sigma = S); zt = m2$series