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1. Consider two MA(1) models: 1 x₁ =W₁ + 2W₁-1₁ Wt ~ N(0, 2²) Ut~ N(0, 1²) Yt = vt + 2vt-1, (a) Why do we prefer invertible models? (b) Check if both models are invertible using the lag operator B. (c) Find the mean functions for both models. (d) Find the autocovariance functions for both models. (e) Find the autocorrelation functions for both models. (f) Simulate 100 observations for each model, and compare the time plots of the simulated series. Set a seed, and use it for both. (g) Which of the two models above is preferred? Give one reason.

1. Consider two MA(1) models: 1 x₁ =W₁ + 2W₁-1₁ Wt ~ N(0, 2²) Ut~ N(0, 1²) Yt = vt + 2vt-1, (a) Why do we prefer invertible models? (b) Check if both models are invertible using the lag operator B. (c) Find the mean functions for both models. (d) Find the autocovariance functions for both models. (e) Find the autocorrelation functions for both models. (f) Simulate 100 observations for each model, and compare the time plots of the simulated series. Set a seed, and use it for both. (g) Which of the two models above is preferred? Give one reason.

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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1. Consider two MA(1) models: xt = Wt+ 1 2Wt-1, N(0, 2²) Ut ~ N(0, 1²) Wt ~ Yt Vt +2Vt-1, (a) Why do we prefer invertible models? (b) Check if both models are invertible using the lag operator B. (c) Find the mean functions for both models. (d) Find the autocovariance functions for both models. (e) Find the autocorrelation functions for both models. (f) Simulate 100 observations for each model, and compare the time plots of the simulated series. Set a seed, and use it for both. (g) Which of the two models above is preferred? Give one reason.
Transcribed Image Text:1. Consider two MA(1) models: xt = Wt+ 1 2Wt-1, N(0, 2²) Ut ~ N(0, 1²) Wt ~ Yt Vt +2Vt-1, (a) Why do we prefer invertible models? (b) Check if both models are invertible using the lag operator B. (c) Find the mean functions for both models. (d) Find the autocovariance functions for both models. (e) Find the autocorrelation functions for both models. (f) Simulate 100 observations for each model, and compare the time plots of the simulated series. Set a seed, and use it for both. (g) Which of the two models above is preferred? Give one reason.
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