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  2. Autoregressive moving-average model - Wikipedia

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

    MATLAB includes functions such as arma, ar and arx to estimate autoregressive, exogenous autoregressive and ARMAX models. See System Identification Toolbox and Econometrics Toolbox for details. Julia has community-driven packages that implement fitting with an ARMA model such as arma.jl.

  3. Box–Jenkins method - Wikipedia

    en.wikipedia.org/wiki/Box–Jenkins_method

    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 ...

  4. 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

  5. Fractional differencing and fractional integration are the same operation with opposite values of d: e.g. the fractional difference of a time series to d = 0.5 can be inverted (integrated) by applying the same fractional differencing operation (again) but with fraction d = -0.5. See GRETL fracdiff function.

  6. Autoregressive conditional heteroskedasticity - Wikipedia

    en.wikipedia.org/wiki/Autoregressive_conditional...

    The lag length p of a GARCH(p, q) process is established in three steps: . Estimate the best fitting AR(q) model = + + + + = + = +. Compute and plot the ...

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  8. Chekhov's gun - Wikipedia

    en.wikipedia.org/wiki/Chekhov's_gun

    A rifle on display. Chekhov's gun (or Chekhov's rifle; Russian: Чеховское ружьё) is a narrative principle that states that every element in a story must be necessary and irrelevant elements should be removed.

  9. Correlogram - Wikipedia

    en.wikipedia.org/wiki/Correlogram

    For example, in time series analysis, a plot of the sample autocorrelations versus (the time lags) is an autocorrelogram. If cross-correlation is plotted, the result is called a cross-correlogram. The correlogram is a commonly used tool for checking randomness in a data set. If random, autocorrelations should be near zero for any and all time ...