AR(p) model starting values?

Jan 2009
405
2
I'm trying to understand the AR(p) time series model, but something is really confusing me.

For example, let's consider an AR(2) model on {X(t): t= 0, 1, 2, ...}.
To me, this is like a recursive formula. Does that mean we always need to specify the starting values for X(0) and X(1) (e.g. X(0) = 5, X(1) =7) in order to use the AR(2) model? With no specified starting values for X(0) and X(1), how can we determine X(2)?

In my textbook, it never mentions any starting values in AR(p) models and that's why I'm puzzled about this.

Hopefully someone can clarify this. Thanks for the help!
 
Jul 2017
17
4
New York
Yes, you have to specify the starting values when simulating the process into the future. Typically, those are the most recent observed values of the process.

When estimating the model on past values, you can treat X(0) and X(1) as two more unknown parameters. You can estimate the whole set of parameters using Maximum Likelihood, for example.