4. Consider the AR(3) model: y, 0.216y,-3 + E, {6)~ WN(0, 1). %3D (a) Find the solutions (roots) of the autoregressive (characteristic) polynomial. Is this model weakly stationary? (b) If z, = (1-...

Extracted text: 4. Consider the AR(3) model: y, 0.216y,-3 + E, {6)~ WN(0, 1). %3D (a) Find the solutions (roots) of the autoregressive (characteristic) polynomial. Is this model weakly stationary? (b) If z, = (1- B)y, where B denotes the backward shifts operator, which (ARIMA) model does z, follow? Is z, stationary? %3D (c) If y2019 = 0.6, y2020 = 0.5 and y2021 = 1, find the (mean-square optimal) forecasts of y2022 and y2023- (d) Compute the autocovariances y(0) and y(1) of (y,).