By Eni Sumarminingsih, Ssi, MM PARAMETER ESTIMATION By Eni Sumarminingsih, Ssi, MM

The Method of Moments Autoregressive Models Consider first the AR(1) case. For this process, we have the simple relationship ρ1 = φ. In the method of moments, ρ1 is equated to r1, the lag 1 sample autocorrelation. Thus we can estimate φ by Now consider the AR(2) case. The relationships between the parameters φ1 and φ2 and various moments are given by the Yule-Walker equations (4.3.13) Setting k = 1 and using ρ0 = 1 and ρ−1 = ρ1, we get The method of moments replaces ρ1 by r1 and ρ2 by r2 to obtain

These linear equations are then solved for

Moving Average Models