Consider the following MA(2) time series process: v. = 5 +a,-0.5a,_, +0.25a,_,, where {at} is a Gaussian white noise series with mean zero and constant variance o2=0.025. a) What are the mean and variance of the time series vt? b) Is the MA(2) model is stationary? Explain. c) Assume that a100= - 0.01 and agg = 0.02 and a98=-0.04. Compute the 1, 2 and 3-step ahead forecasts of the MA(2) series at the forecast origin t=100. d) Identify the number of autocorrelation coefficients for the MA(2) model that are not zero and compute them