Materi Analisis Deret Waktu

(1)

Page 1

Autoregressive

Process

(2)

(3)

Page 3

(4)

(5)

(6)

• 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

(7)

(8)

(9)

(10)

(11)

(12)

The General Linear Process Version of the AR(1) Model

…1

Y_t-1 = Y_t-2 + e_t-1 …2

(13)

(14)

(15)

(16)

(17)

Page 17

The Autocorrelation Function for the AR(2) Process

(18)

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

(19)

(20)

(21)

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 σ_e2 _{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

(22)