Time series regression

You have a time series of observations of some variable Yt. Consider regressing Yt on lagged observations of Yt. Yt= a + by t-1 + et Show that the estimated b is the same as autocorrelation coefficient p between Yt and Yt-1 P= Cprr(yt,yt-1) tks :slight_smile:

From your notes, b = Cov(y[t], y[t-1])/Var(y[t-1]) = p * Stddev(y[t])*Stddev(y[t-1])/Var(y[t-1]) But Stddev(y[t]) = Stddev(y[t-1]) (at least as t -> inf) because each is just the std dev of the observations. => everything cancels except the p