To calculate the ac.f. of the process, we use the Yule-Walker equation to give , which yields . For , the Yule-Walker equations are , which indicates the auxiliary equation with roots . Using and , some algebra gives Figure 2: Series (top) and autocorrelation functions (bottom) of the process . Example Consider the AR(2) process by is this process stationary? If so, what is its ac.f.? Solutions: (1) The roots of are 4 and -3, which are outside the unit circle, hence is stationary. (2) The ACFs of are Where . Exercises Suppose are independent normal random variables with mean 0 and variance . Compute the ac.f. of the AR(2) process Solutions: Some useful models ARMA models –
To calculate the ac.f. of the process, we use the Yule-Walker equation to give , which yields . For , the Yule-Walker equations are , which indicates the auxiliary equation with roots . Using and , some algebra gives Figure 2: Series (top) and autocorrelation functions (bottom) of the process . Example Consider the AR(2) process by is this process stationary? If so, what is its ac.f.? Solutions: (1) The roots of are 4 and -3, which are outside the unit circle, hence is stationary. (2) The ACFs of are Where . Exercises Suppose are independent normal random variables with mean 0 and variance . Compute the ac.f. of the AR(2) process Solutions: Some useful models – ARMA models
SomeTSModels.docx