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The notation () indicates an autoregressive model of order p.The AR(p) model is defined as = = + where , …, are the parameters of the model, and is white noise. [1] [2] This can be equivalently written using the backshift operator B as
Autocorrelation of white noise [ edit ] The autocorrelation of a continuous-time white noise signal will have a strong peak (represented by a Dirac delta function ) at τ = 0 {\displaystyle \tau =0} and will be exactly 0 {\displaystyle 0} for all other τ {\displaystyle \tau } .
Decorrelation is a general term for any process that is used to reduce autocorrelation within a signal, or cross-correlation within a set of signals, while preserving other aspects of the signal. [ citation needed ] A frequently used method of decorrelation is the use of a matched linear filter to reduce the autocorrelation of a signal as far ...
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 ...
In stochastic processes, chaos theory and time series analysis, detrended fluctuation analysis (DFA) is a method for determining the statistical self-affinity of a signal. It is useful for analysing time series that appear to be long-memory processes (diverging correlation time, e.g. power-law decaying autocorrelation function) or 1/f noise.
White noise: The partial autocorrelation is 0 for all lags. Autoregressive model: The partial autocorrelation for an AR(p) model is nonzero for lags less than or equal to p and 0 for lags greater than p. Moving-average model: If , >, the partial autocorrelation oscillates to 0.
MUSIC outperforms simple methods such as picking peaks of DFT spectra in the presence of noise, when the number of components is known in advance, because it exploits knowledge of this number to ignore the noise in its final report.
First, white noise is a generalized stochastic process with independent values at each time. [12] Hence it plays the role of a generalized system of independent coordinates, in the sense that in various contexts it has been fruitful to express more general processes occurring e.g. in engineering or mathematical finance, in terms of white noise.