Ar(2) model example

1. What is an AR 2 process?
2. How do you show AR 2 is stationary?
3. Is AR 2 stationary?
4. Is AR 2 causal?

What is an AR 2 process?

An AR(1) autoregressive process is one in which the current value is based on the immediately preceding value, while an AR(2) process is one in which the current value is based on the previous two values. An AR(0) process is used for white noise and has no dependence between the terms.

How do you show AR 2 is stationary?

1. The stationarity condition is: two solutions of x from φ(x) = 1−φ1x−φ2x2 = 0 are outside the unit circle. 2. Rewriting the AR(2) model, (1 − φ1L − φ2L2)yt = ϵt.

Is AR 2 stationary?

c. The AR(2) process

When these solutions, in absolute value, are smaller than 1, the AR(2) model is stationary. The derivation of the theoretical ACF and PACF for an AR(2) model is described below.

Is AR 2 causal?

AR(2) model is causal.