Autoregressive Integrated Moving Average
In statistics and econometrics, and in particular in time series analysis, an autoregressive integrated moving average (ARIMA) model is a generalization of an autoregressive moving average (ARMA) model. These models are fitted to time series data either to better understand the data or to predict future points in the series (forecasting). They are applied in some cases where data show evidence of non-stationarity, where an initial differencing step (corresponding to the "integrated" part of the model) can be applied to remove the non-stationarity.
The model is generally referred to as an ARIMA(p,d,q) model where p, d, and q are non-negative integers that refer to the order of the autoregressive, integrated, and moving average parts of the model respectively. ARIMA models form an important part of the Box-Jenkins approach to time-series modelling.
When one of the three terms is zero, it's usual to drop "AR", "I" or "MA". For example, ARIMA(0,1,0) is I(1), and ARIMA(0,0,1) is MA(1).
Read more about Autoregressive Integrated Moving Average: Definition, Other Special Forms, Forecasts Using ARIMA Models, Examples, Implementations in Statistics Packages
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