Description

rt = 0.01 + 0.6rt−1− 0.4rt−2 + at,
where {at} is a white noise series with mean zero and variance 0.02.
(a) What is the mean of the return series rt?
(b) Compute the lag-1, lag-2 and lag-3 autocorrelations of rt.
(c) Simulate a time series of length T = 2000 from this model. Creat a time series plot, and a sample autocorrelation plot. Compute the lag-1, lag-2 and lag-3 sample autocorrelations.
(d) (Bonus 5 pts). Compute the variance, lag-1 and lag-2 autocovariances of rt. What are the corresponding sample autocovariances?
2. Suppose we have the following estimates from the data:
µˆ = 0.5768, γˆ0 = 1.7379, γˆ1 = 1.4458, γˆ2 = 1.0600.
Find the Yule-Walker estimates for the AR(2) model.
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