Integration

Integration may refer to:

Sociology and economy

Mathematics

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 reduce the non-stationarity.

Non-seasonal ARIMA models are generally denoted where parameters p, d, and q are non-negative integers, is the order of the Autoregressive model, is the degree of differencing, and is the order of the Moving-average model. Seasonal ARIMA models are usually denoted , where refers to the number of periods in each season, and the uppercase refer to the autoregressive, differencing, and moving average terms for the seasonal part of the ARIMA model. ARIMA models form an important part of the Box-Jenkins approach to time-series modelling.