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2. Consider the ARMA(1,1) process: xt = axt-1 + Wt + Bwt-1, where we is white noise. (a) Write an R function that calculates the autocorrelation function Pk = ak-1(a + 3)(1+aß) 1 + 2aß + 3² k≥ 1 (b) Plot the autocorrelation function for a = 0.7 and 3 = -0.5 for lags 0 to 20. (c) Simulate n = 100 values of the ARMA(1,1) model with a = 0.7 and 3 = -0.5, and compare the sample correlogram to the theoretical correlogram. Use w~ N(0, 1). (d) Repeat part (c) for n = 1000.

2. Consider the ARMA(1,1) process: xt = axt-1 + Wt + Bwt-1, where we is white noise. (a) Write an R function that calculates the autocorrelation function Pk = ak-1(a + 3)(1+aß) 1 + 2aß + 3² k≥ 1 (b) Plot the autocorrelation function for a = 0.7 and 3 = -0.5 for lags 0 to 20. (c) Simulate n = 100 values of the ARMA(1,1) model with a = 0.7 and 3 = -0.5, and compare the sample correlogram to the theoretical correlogram. Use w~ N(0, 1). (d) Repeat part (c) for n = 1000.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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2. Consider the ARMA(1,1) process: xt = axt-1 + wt + Bwt-1, where wt is white noise. (a) Write an R function that calculates the autocorrelation function ak-¹(a + 3)(1+aß) 1 + 2aß + 3² Pk = " k≥ 1 (b) Plot the autocorrelation function for a = 0.7 and 3 = -0.5 for lags 0 to 20. (c) Simulate n = 100 values of the ARMA(1,1) model with a = 0.7 and 3= -0.5, and compare the sample correlogram to the theoretical correlogram. Use wt ~ N(0,1). (d) Repeat part (c) for n = 1000.
Transcribed Image Text:2. Consider the ARMA(1,1) process: xt = axt-1 + wt + Bwt-1, where wt is white noise. (a) Write an R function that calculates the autocorrelation function ak-¹(a + 3)(1+aß) 1 + 2aß + 3² Pk = " k≥ 1 (b) Plot the autocorrelation function for a = 0.7 and 3 = -0.5 for lags 0 to 20. (c) Simulate n = 100 values of the ARMA(1,1) model with a = 0.7 and 3= -0.5, and compare the sample correlogram to the theoretical correlogram. Use wt ~ N(0,1). (d) Repeat part (c) for n = 1000.
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