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In time series analysis used in statistics and econometrics, autoregressive integrated moving average (ARIMA) and seasonal ARIMA (SARIMA) models are generalizations of the autoregressive moving average (ARMA) model to non-stationary series and periodic variation, respectively.
See System Identification Toolbox and Econometrics Toolbox for details. Julia has community-driven packages that implement fitting with an ARMA model such as arma.jl. Python has the statsmodelsS package which includes many models and functions for time series analysis, including ARMA.
In an ARIMA model, the integrated part of the model includes the differencing operator (1 − B) (where B is the backshift operator) raised to an integer power.For example,
statsmodels – Python package for statistics and econometrics (regression, plotting, hypothesis testing, generalized linear model (GLM), time series analysis, autoregressive–moving-average model (ARMA), vector autoregression (VAR), non-parametric statistics, ANOVA) Statistical Lab – R-based and focusing on educational purposes
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The original model uses an iterative three-stage modeling approach: Model identification and model selection: making sure that the variables are stationary, identifying seasonality in the dependent series (seasonally differencing it if necessary), and using plots of the autocorrelation (ACF) and partial autocorrelation (PACF) functions of the dependent time series to decide which (if any ...
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X-13ARIMA-SEATS, successor to X-12-ARIMA and X-11, is a set of statistical methods for seasonal adjustment and other descriptive analysis of time series data that are implemented in the U.S. Census Bureau's software package. [3]