extensions A number of variations on the ARIMA model are commonly employed. If multiple time series are used then the can be thought of as vectors and a VARIMA model may be appropriate. Sometimes a seasonal effect is suspected in the model; in that case, it is generally considered better to use a SARIMA (seasonal ARIMA) model than to increase the order of the AR or MA parts of the model. If the time-series is suspected to exhibit long-range dependence, then the d parameter may be allowed to have non-integer values in an autoregressive fractionally integrated moving average model, which is also called a Fractional ARIMA (FARIMA or ARFIMA) model. Software implementations Various packages that apply methodology like Box–Jenkins parameter optimization are available to find the right parameters for the ARIMA model. EViews: has extensive ARIMA and SARIMA capabilities. Julia: contains an ARIMA implementation in the TimeModels package Mathematica: includes ARIMAProcess function. MATLAB: the Econometrics Toolbox includes ARIMA models and regression with ARIMA errors NCSS: includes several procedures for ARIMA fitting and forecasting. Python: the "statsmodels" package includes models for time series analysis – univariate time series analysis: AR, ARIMA – vector autoregressive models, VAR and structural VAR – descriptive statistics and process models for time series analysis. R: the standard R stats package includes an arima function, which is documented in "ARIMA Modelling of Time Series". Besides the part, the function also includes seasonal factors, an intercept term, and exogenous variables (xreg, called "external regressors"). The CRAN task view on Time Series is the reference with many more links. The "forecast" package in R can automatically select an ARIMA model for a given time series with the function and can also simulate seasonal and non-seasonal ARIMA models with its function. Ruby: the "statsample-timeseries" gem is used for time series analysis, including ARIMA models and Kalman Filtering. JavaScript: the "arima" package includes models for time series analysis and forecasting (ARIMA, SARIMA, SARIMAX, AutoARIMA) C: the "ctsa" package includes ARIMA, SARIMA, SARIMAX, AutoARIMA and multiple methods for time series analysis. SAFE TOOLBOXES: includes ARIMA modelling and regression with ARIMA errors. SAS: includes extensive ARIMA processing in its Econometric and Time Series Analysis system: SAS/ETS. IBM SPSS: includes ARIMA modeling in its Statistics and Modeler statistical packages. The default Expert Modeler feature evaluates a range of seasonal and non-seasonal autoregressive (p), integrated (d), and moving average (q) settings and seven exponential smoothing