Page 1
Autoregressive
Process
Page 3
• Since |
| < 1 , the magnitude of the
autocorrelation function decreases
exponentially as the number of lags,
k
,
increases.
• If 0 <
<1, all correlations are positive;
• If -1 <
< 0, the lag 1 autocorrelation is
negative (ρ
1=
) and the signs of successive
autocorrelations alternate from positive to
negative, with their magnitudes decreasing
exponentially.
• Portions of the graphs of several
The General Linear Process Version of the AR(1) Model
…1
Yt-1 = Yt-2 + et-1 …2
Page 17
The Autocorrelation Function for the AR(2) Process
Equations (4.3.12) and/or (4.3.13) are usually called the Yule-Walker
equations, especially the set of two equations obtained for k = 1 and 2.
Setting k = 1 and using ρ0 = 1
Page 21
The Variance for the AR(2) Model
The process variance γ0 can be expressed in terms of the model parameters
1, 2, and σe2 as follows: Taking the variance of both sides of Equation (4.3.9)
yields
Setting k = 1 in Equation (4.3.12) gives a second linear equation for γ0 and γ1