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  2. 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 ...

  3. Autoregressive moving-average model - Wikipedia

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

    The notation ARMAX(p, q, b) refers to a model with p autoregressive terms, q moving average terms and b exogenous inputs terms. The last term is a linear combination of the last b terms of a known and external time series . It is given by:

  4. Box–Jenkins method - Wikipedia

    en.wikipedia.org/wiki/Box–Jenkins_method

    In time series analysis, the Box–Jenkins method, [1] named after the statisticians George Box and Gwilym Jenkins, applies autoregressive moving average (ARMA) or autoregressive integrated moving average (ARIMA) models to find the best fit of a time-series model to past values of a time series.

  5. Autoregressive integrated moving average - Wikipedia

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

    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.

  6. 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 ...

  7. STAR model - Wikipedia

    en.wikipedia.org/wiki/STAR_model

    Exponential transition function for the ESTAR model with varying from -10 to +10 and - from 0 to 1.. In statistics, Smooth Transition Autoregressive (STAR) models are typically applied to time series data as an extension of autoregressive models, in order to allow for higher degree of flexibility in model parameters through a smooth transition.

  8. Moving-average model - Wikipedia

    en.wikipedia.org/wiki/Moving-average_model

    [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 ...

  9. SETAR (model) - Wikipedia

    en.wikipedia.org/wiki/SETAR_(model)

    SETAR models were introduced by Howell Tong in 1977 and more fully developed in the seminal paper (Tong and Lim, 1980). They can be thought of in terms of extension of autoregressive models, allowing for changes in the model parameters according to the value of weakly exogenous threshold variable z t, assumed to be past values of y, e.g. y t-d, where d is the delay parameter, triggering the ...