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  2. Autoregressive integrated moving average - Wikipedia

    en.wikipedia.org/wiki/Autoregressive_integrated...

    Non-seasonal ARIMA models are usually denoted ARIMA(p, d, q) where parameters p, d, q are non-negative integers: p is the order (number of time lags) of the autoregressive model, d is the degree of differencing (the number of times the data have had past values subtracted), and q is the order of the moving-average model. Seasonal ARIMA models ...

  3. Box–Jenkins method - Wikipedia

    en.wikipedia.org/wiki/Box–Jenkins_method

    Instead, one includes the order of the seasonal terms in the model specification to the ARIMA estimation software. However, it may be helpful to apply a seasonal difference to the data and regenerate the autocorrelation and partial autocorrelation plots. This may help in the model identification of the non-seasonal component of the model.

  4. Autoregressive moving-average model - Wikipedia

    en.wikipedia.org/wiki/Autoregressive_moving...

    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. Seasonal ARIMA (SARIMA or periodic ARMA) models periodic variation.

  5. Exponential smoothing - Wikipedia

    en.wikipedia.org/wiki/Exponential_smoothing

    The default Expert Modeler feature evaluates all seven exponential smoothing models and ARIMA models with a range of nonseasonal and seasonal p, d, and q values, and selects the model with the lowest Bayesian Information Criterion statistic. Stata: tssmooth command [19] LibreOffice 5.2 [20] Microsoft Excel 2016 [21]

  6. Autoregressive model - Wikipedia

    en.wikipedia.org/wiki/Autoregressive_model

    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 ...

  7. In statistics, autoregressive fractionally integrated moving average models are time series models that generalize ARIMA (autoregressive integrated moving average) models by allowing non-integer values of the differencing parameter.

  8. Stationary process - Wikipedia

    en.wikipedia.org/wiki/Stationary_process

    Another type of non-stationary process, distinct from those with trends, is a cyclostationary process, which exhibits cyclical variations over time. Strict stationarity, as defined above, can be too restrictive for many applications. Therefore, other forms of stationarity, such as wide-sense stationarity or N-th-order stationarity, are often used.

  9. X-13ARIMA-SEATS - Wikipedia

    en.wikipedia.org/wiki/X-13ARIMA-SEATS

    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]