Which of the following conditions is necessary for a time series to be considered weakly stationary?
Question 2
Given an AR(2) model: $Y_t = \phi_1 Y_{t-1} + \phi_2 Y_{t-2} + \epsilon_t$. If the characteristic equation has roots outside the unit circle, what does this imply about the stationarity of the process?
Question 3
In the context of spectral analysis, what is the primary advantage of using a smoothed periodogram (e.g., using a tapering window) over a raw periodogram?
Question 4
Consider a state-space model defined by the state equation $x_t = F x_{t-1} + G w_t$ and the observation equation $y_t = H x_t + v_t$. If the system is observable, what does this imply about the matrices H and F?
Question 5
When using cross-validation for time series model validation, why is it generally inappropriate to use standard k-fold cross-validation, and what alternative is preferred?
