Materi Analisis Deret Waktu

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 ρ 1 by r1 and ρ2 by r2 to obtain

These linear equations are then solved for

Moving Average Models