R Statistics Cookbook

The general ARIMA model

Time series analysis deals with several models, but ARIMA models are the most used ones. ARIMA means autoregressive integrated moving average. That implies that the model relies on two mathematical artefacts (autoregressive (AR) and moving-average (MA) processes) to model temporal phenomena. ARIMA is, thus, deeply rooted in stochastic processes, and what we will do is find a reasonable stochastic process (a combination of AR and MA processes) that matches the empirical autocovariance structure that we see in the data. AR processes are structured as Yt = c1 Yt-1 + … + ck Yt-k + et, where et is Gaussian noise. On the other hand, MA processes are structured as Yt = c1 et-1 +…+ck et-k + et.

AR, MA and ARMA processes have ...