Consider the model as yt= βyt-1 +et, which describes the dynamics of price of a company’s...

Consider the model as y_t= βy_t-1 +e_t, which describes the dynamics of price of a company’s stock (y).

a. Assuming that e_t has zero mean, constant variance σ_e² and is not serially correlated, obtain expressions for E(y_t), var(y_t) and cov(y_t, y_t-1 ) and the first-order auto correlation coefficient. Does y represent a stationary process? Explain briefly.

b. If now e_t follows an AR(1) process, that is e_t =ρe_t-1 +v_t, where v_t is white noise and 0 < ρ < 1, is this process stationary? Show your work.

c. Given b, show how you would get GLS estimates, assuming the sample is small, and you do not want to lose any observations?

d. Show that the GLS model can be written as an AR(2) model for T> 1.

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orchestra answered 2 years ago

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