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Please provide the R codes1 Simulate an AR(1) time series of length n = 36 with φ = 0.7.
(a) Calculate and plot the theoretical autocorrelation function for this model. Plot sufficient lags until the correlations are negligible.
(b) Calculate and plot the sample ACF for your simulated series. How well do the values and patterns match the theoretical ACF from part (a)?
(c) What are the theoretical partial autocorrelations for this model?
(d) Calculate and plot the sample ACF for your simulated series. How well do the values and patterns match the theoretical ACF from part (a)? Use the large-sample standard errors reported in Exhibit 6.1 on page 111, to quantify your answer.
(e) Calculate and plot the sample PACF for your simulated series. How well do the values and patterns match the theoretical ACF from part (c)? Use the large-sample standard errors reported on page 115 to quantify your answer.
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