Question: (a) Simulate a time series of ???? = 200 observations from an IMA(0, 2, 2) model with parameters ????1 = 0.8 and ????2 = 0.4

(a) Simulate a time series of ???? = 200 observations from an IMA(0, 2, 2) model with parameters ????1 = 0.8 and ????2 = −0.4 using the arima.sim() function in R; type help(arima.sim) for details. Plot the resulting series and comment on its behavior.

(b) Estimate and plot the autocorrelation function of the simulated time series.

(c) Estimate and plot the autocorrelation functions of the first and second differences of the series.

(d) Comment on the patterns of the autocorrelation functions generated above. Are the results consistent with what you would expect to see for this IMA(0, 2, 2)

process?

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