In time series analysis, an autoregressive integrated moving average (ARIMA) model is a generalization of an autoregressive moving average (ARMA) model. In theory, the most general class of models for forecasting a time series are stationary and can be made stationary by transformations such as differencing and logging. ARIMA models form an important part of the Box-Jenkins approach to time-series modeling. A non-seasonal ARIMA model is classified as an ARIMA (p, d, q) model, where: p is the number of autoregressive terms, d is the number of non-seasonal differences and q is the number of moving average terms.
Estimation
At the identification stage one or more models are tentatively chosen that seem to provide statistically adequate representations of the available data. The parameters are estimated by modified least squares or the maximum likelihood techniques appropriate to time series data.
Diagnostic
For adequacy of the model, the residuals are examined from the fitted model and alternative models are considered. Different models can be obtained for various combinations of AR and MA individually and collectively. The satisfactory model is considered which adequately fits the data.
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