# a) Show that the series {x t } given by x t = x t-1 – x t-2 + w t is nonstationary. b) Write down…

a) Show that the series {xt} given by xt = xt−1xt−2 + wt is nonstationary.

b) Write down the model for {yt}, where yt = ∇xt. Show that {yt} is stationary.

c) Simulate a series of 1000 values for {xt}, placing the simulated data in x, and use these simulated values to produce a series of 999 values for {yt}, placing this series in the vector y.

d) Fit an AR model to y. Give the fitted model parameter estimates and a 95% confidence interval for the underlying model parameters based on these estimates. Compare the confidence intervals to the parameters used to simulate the data and explain the results.

e) Plot the correlogram of the residuals of the fitted model and comment.

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