Suppose that the stationary time series xt t T satisfies the

Suppose that the stationary time series {x_t: t T} satisfies the equation: x_t = beta x_t - 3 + u_t where {u_t : t T} is a white noise time series with variance sigma^2: = 9.0. Find the autocorrelation function of {x_t: t T}. Plot the autocorrelation function with beta = 0.8.

Solution

autocorrelation function of Xt : t e T

will be

9.0 / 3 = 3

autocorrelation function with betha = 0.8

9 / 0.8 = 11.25