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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.
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 ...
Vector AR (VAR) and vector ARMA (VARMA) model multivariate time series. Autoregressive integrated moving average (ARIMA) models non-stationary time series (that is, whose mean changes over time). Autoregressive conditional heteroskedasticity (ARCH) models time series where the variance changes.
These models are useful in modeling time series with long memory—that is, in which deviations from the long-run mean decay more slowly than an exponential decay. The acronyms "ARFIMA" or "FARIMA" are often used, although it is also conventional to simply extend the "ARIMA( p , d , q )" notation for models, by simply allowing the order of ...
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]
Together with the moving-average (MA) model, it is a special case and key component of the more general autoregressive–moving-average (ARMA) and autoregressive integrated moving average (ARIMA) models of time series, which have a more complicated stochastic structure; it is also a special case of the vector autoregressive model (VAR), which ...
Download as PDF; Printable version ... Time series forecasting is the use of a model to predict future ... (ARMA) and autoregressive integrated moving-average (ARIMA ...
[1] [2] The moving-average model specifies that the output variable is cross-correlated with a non-identical to itself random-variable. Together with the autoregressive (AR) model, the moving-average model is a special case and key component of the more general ARMA and ARIMA models of time series, [3] which have a more complicated stochastic ...