A Complete Introduction To Time Series Analysis (with R):: Prediction III: Forecasting with ARMA(p,q) models
We have come a long way from first exploring the idea of models with way too little or too much dependence, to the structured ARMA(p,q) models that aim to balance this by taking into account not only dependence between observations, but between their random noise at different timesteps. In the “Prediction II: Forecasting” section, we studied the best linear predictor along with two algorithms to help us find the BLP coefficients and make predictions: the Durbin-Levinson algorithm and the Innovations algorithm. In this article, we will see how to extend these ideas to produce predictions for ARMA(p,q) models. Before starting, I strongly suggest you review the first article on the Innovations algorithm since this one builds directly on that one. Let’s now get into it!
Innovations Algorithm for ARMA(p,q)
where the theta coefficients are determined by the recursive computations
