What are the mean and variance of the return series rt

Question

Suppose that the daily log return of a security follows the model

where {a_t} is a Gaussian white noise series with mean zero and variance 0.02.

What are the mean and variance of the return series r_t?

Compute the lag-1 and lag-2 autocorrelations of r_t. Assume that r₁₀₀ = -0.01, and r₉₉ = 0.02.

Compute the 1-step and 2-step ahead forecasts of the return series at the forecast origin t = 100.

What are the associated standard deviations of the forecast errors?