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  2. Autoregressive moving-average model - Wikipedia

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

    The general ARMA model was described in the 1951 thesis of Peter Whittle, who used mathematical analysis (Laurent series and Fourier analysis) and statistical inference. [ 12 ] [ 13 ] ARMA models were popularized by a 1970 book by George E. P. Box and Jenkins, who expounded an iterative ( Box–Jenkins ) method for choosing and estimating them.

  3. Moving-average model - Wikipedia

    en.wikipedia.org/wiki/Moving-average_model

    In time series analysis, the moving-average model (MA model), also known as moving-average process, is a common approach for modeling univariate time series. [ 1 ] [ 2 ] The moving-average model specifies that the output variable is cross-correlated with a non-identical to itself random-variable.

  4. Time series - Wikipedia

    en.wikipedia.org/wiki/Time_series

    Time series analysis comprises methods for analyzing time series data in order to extract meaningful statistics and other characteristics of the data. Time series forecasting is the use of a model to predict future values based on previously observed values.

  5. Box–Jenkins method - Wikipedia

    en.wikipedia.org/wiki/Box–Jenkins_method

    For many series, the period is known and a single seasonality term is sufficient. For example, for monthly data one would typically include either a seasonal AR 12 term or a seasonal MA 12 term. For Box–Jenkins models, one does not explicitly remove seasonality before fitting the model.

  6. 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.

  7. 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 ...

  8. Singular spectrum analysis - Wikipedia

    en.wikipedia.org/wiki/Singular_spectrum_analysis

    In time series analysis, singular spectrum analysis (SSA) is a nonparametric spectral estimation method. It combines elements of classical time series analysis, multivariate statistics , multivariate geometry, dynamical systems and signal processing .

  9. Linear model - Wikipedia

    en.wikipedia.org/wiki/Linear_model

    An example of a linear time series model is an autoregressive moving average model.Here the model for values {} in a time series can be written in the form = + + = + =. where again the quantities are random variables representing innovations which are new random effects that appear at a certain time but also affect values of at later times.