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  2. Autoregressive model - Wikipedia

    en.wikipedia.org/wiki/Autoregressive_model

    The autoregressive model specifies that the output variable depends linearly on its own previous values and on a stochastic term (an imperfectly predictable term); thus the model is in the form of a stochastic difference equation (or recurrence relation) which should not be confused with a differential equation.

  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 d t {\displaystyle d_{t}} .

  4. Vector autoregression - Wikipedia

    en.wikipedia.org/wiki/Vector_autoregression

    Continuing the above example, a 5th-order VAR would model each year's wheat price as a linear combination of the last five years of wheat prices. A lag is the value of a variable in a previous time period. So in general a pth-order VAR refers to a VAR model which includes lags for the last p time periods.

  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. Box–Jenkins method - Wikipedia

    en.wikipedia.org/wiki/Box–Jenkins_method

    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. Instead, one includes the order of the seasonal terms in the model specification to the ARIMA estimation software. However, it may be ...

  7. Lag operator - Wikipedia

    en.wikipedia.org/wiki/Lag_operator

    Polynomials of the lag operator can be used, and this is a common notation for ARMA (autoregressive moving average) models. For example, = = = (=) specifies an AR(p) model.A polynomial of lag operators is called a lag polynomial so that, for example, the ARMA model can be concisely specified as

  8. In an ARIMA model, the integrated part of the model includes the differencing operator (1 − B) (where B is the backshift operator) raised to an integer power.For example,

  9. Unit root - Wikipedia

    en.wikipedia.org/wiki/Unit_root

    The first order autoregressive model, = +, has a unit root when =.In this example, the characteristic equation is =.The root of the equation is =.. If the process has a unit root, then it is a non-stationary time series.