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.