ARIMA Time Series Models

Abstract

The autoregressive moving average (ARMA) model defined as

$$X_{t} = \nu + \alpha _{1}X_{t-1} + \ldots + \alpha _{p}X_{t-p} + \beta _{1}\epsilon _{t-1} + \ldots + \beta _{q}\epsilon _{t-q} + \epsilon _{t},$$

deals with linear time series. The time series should be a covariance stationary process. It consists of two parts, an autoregressive (AR) part of order p and a moving average (MA) part of order q. When an ARMA model is not stationary, the methods of analyzing stationary time series cannot be used directly. In order to handle those processes within the framework of the classical time series analysis, we must first form the differences to get a stationary process.

Time does not wait for anyone.