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If the forecasting method is working correctly, successive innovations are uncorrelated with each other, i.e., constitute a white noise time series. Thus it can be said that the innovation time series is obtained from the measurement time series by a process of 'whitening', or removing the predictable component.
A value H in the range 0.5–1 indicates a time series with long-term positive autocorrelation, meaning that the decay in autocorrelation is slower than exponential, following a power law; for the series it means that a high value tends to be followed by another high value and that future excursions to more high values do occur. A value in the ...
White noise draws its name from white light, [2] although light that appears white generally does not have a flat power spectral density over the visible band. An image of salt-and-pepper noise In discrete time , white noise is a discrete signal whose samples are regarded as a sequence of serially uncorrelated random variables with zero mean ...
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 ...
In time series analysis used in statistics and econometrics, ... (0, 0, 0) model is a white noise model. ... Java and Python.
If a time series {} is ... The autocorrelation of a continuous-time white noise signal will have a strong peak (represented by a Dirac delta function) ...
The transformation is called "whitening" because it changes the input vector into a white noise vector. Several other transformations are closely related to whitening: the decorrelation transform removes only the correlations but leaves variances intact, the standardization transform sets variances to 1 but leaves correlations intact,
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 ...