- ARMA model is a stochastic version of recursive relation. For deterministic recursive relations, we solve them and need initial conditions to fully get the solution. So I wonder what is an "initial condition" for ARMA model like?
- In Introduction to Time Series and Forecasting, by Peter J. Brockwell, Richard A. Davis, they define an ARMA model to be causal, if its output process can be represented as MA($\infty$) (see equation (3.1.5)). In equation (3.1.7), they gave the explicit formulation of the MA($\infty$) representation. I don't find they specify or use any "initial" condition in the definition of causality and in the derivation of the MA($\infty$) representation. This is quite different from that we need initial conditions to fully get the solution to a deterministic recursive relation. So how shall we understand the MA($\infty$) representation of an ARMA output process?