Description

Prediction
1. (30 points)
(a) Simulate a 200 point sample from an AR(4) process {Xt} with ϕ1 = .8, ϕ2 = .2, ϕ3 = −.2, ϕ4 = −.1 and with {Zt}∼ WN(0,1) with Zt ∼ N(0,1). (see
Example 3.4.3). Plot the sample with appropriately labeled axes.
(b) Plot the sample acf versus lag. Are there significant linear dependencies for lags greater than 1? Explain your answer.
(c) Compare one step predictions from the original data: Using the data , compute estimated one step predictions
,
and plot the predictions and the original data using different colors for the two series on the same graph (see Figures 1 and 2 for Example 3.4.2).
(d) Compute predictions into the future: Using a software package that computes the best linear MSE predictor, compute the predictions
.
Plot the predictions together with the original data.
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