Question

3.3 Suppose Y, = u + en +-1. Find Var(Y). Compare your answer to what would have been obtained if Y, = u + ez. Describe the effect that the autocorrelation in {Y,} has on Var(7).

Answer 1

tee-1 we know that 1- (ut ex tet-1) then Expected value et y is and variance is Var.cy) - vare It â Cuveet een] to a ver (let ete-I) [Ver? (ll) + Varlett +1eur (ex-r)] = 1 n lotto Vonly) = qoca) - Similarly, it /= ultet then vor (9) Tel Conguine nation (1950, we obtained that

{ variance et Y, - et eft®:--).+ 2 variarxe dr Yer sheet Autolaelaton 3- The stationary time series y has, by detinentia on, a stable autovariance function COV LYE YE-1) = N(1), for all integers to Since for any. Par oto Mondom Vožoble Yt and Coulye Y-1) = COV.LYENYED Varr (V4 )* Vor (9-12 and since Vot(Yu) = Vor (Yt-j) = 1601 it follows that con (Y6 Y6-1) = (1 = Pcil *. we call put the autocarelation function. As per ewation 3), te obtect that the autocarelation in It's has on Vaily) if varly) is increase then autocreta tion is decrease and vice - Versa.

Given the model, Think of autocorrelation as signifying a systematic relationship between the residuals measured at different points in time This could be caused by inertia in economic variables, incorrect functional form or data interpolation/revision The effect is that $Cov(Y_{t}, Y_{t-1}) \neq 0$ .