2. Finance
3. consider the following ma2 process zt ut 1ut1...

# Question: consider the following ma2 process zt ut 1ut1...

###### Question details

Consider the following MA(2) process: , where ut is a zero-mean white noise process with variance ${\sigma }^{2}$.

(a) Calculate the conditional and unconditional means of ${z}_{t}$, that is, ${E}_{t}\left[{z}_{t+1}\right]$ and E[${z}_{t}$].

(b) Calculate the conditional and unconditional variances of ${z}_{t}$, that is, $Va{r}_{t}\left[{z}_{t+1}\right]$ and Var[${z}_{t}$].

(c) Derive the autocorrelation function of this process for all lags as functions of the parameters ${\alpha }_{1}$ and ${\alpha }_{2}$