Consider the time series:xₜ= β₁+ β₂t + wₜwhere β1 and β2 are known constants and wₜ is a white noise process with variance σ ²_w.(a) Determine whether xₜ is stationary.(b) Show that the process yₜ= xₜ

Consider the time series:xₜ= β₁+ β₂t + wₜwhere β1 and β2 are known constants and wₜ is a white noise process with variance σ ²_w.(a) Determine whether xₜ is stationary.(b) Show that the process yₜ= xₜ − xₜ₋₁ is stationary.(c) Show that the mean of the moving averagevt = [1 /2q + 1] (j=-q→q) Σ xₜ₋ⱼis β₁ + β₂t, and give a simplified expression for the autocovariance function.

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