Sample Question #108 (econometrics – time series)
Consider the process
yt = εt + βεt-1εt-2, t = 1, …, T
where εt is a sequence of i.i.d. random variables with mean zero and constant variance, and ε0 = ε-1 = 0.
Show that yt is white noise. What is the MMSE (minimum mean squared-error estimator) of yT+1? What about the MMSLE (minimum mean squared-error linear estimator)?
[Taken from exercise 6.10 of Harvey, Forecasting, Structural Time Series Models and the Kalman Filter]