Suppose yt follows a stationaryAR(1)model withARparameter and innovationvariance v. De ne x= (y1 yn).We knowthat x N(0s n)wheres=v (1 2) is themarginal varianceof the ytprocessandthecorrelationmatrix nhas(i j)element i j viz.

n=

1 2 n 1 1 n 2 2 1 n 3 n 1 n 2 n 3 1 FindtheprecisionmatrixKn=s 1 1 n andcommentonitsform.

Hint:Oneway to nd this is brute-force matrix inversionusing in duction;but, that is just linearalgebrathat inparticular ignores the probabilitymodel thatde nes n.Thereisasimplerandmoreinstruc tivewaytoidentifyKnbasedonre ectingontheprobabilitymodel.