Definition White Noise Error Term
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Meaning Of White Noise
vote favorite 6 What is the best way of defining white noise process so it is intuitive and easy to understand? time-series share|improve this question edited Aug 20 '12 at 6:18 mpiktas 24.7k448103 asked Feb 10 '11 at 22:13 user333 1,85373044 add a comment| 3 Answers 3 active oldest votes up vote 12 down vote accepted A white noise process is one with a mean zero and no correlation between its values at different times. See the 'white random process' white noise process stationary section of Wikipedia's article on white noise. share|improve this answer answered Feb 10 '11 at 22:23 onestop 14.3k23564 When you say correlation between values at different times... do you think all possible lag combinations or only t vs t-1? –user333 Feb 10 '11 at 22:37 @user333 All nonzero lags: that's the first equation in the Wikipedia link @onestop gave. –whuber♦ Feb 10 '11 at 22:40 1 you forgot the constant variation. If variation varies, then the process is not white noise. –mpiktas Feb 11 '11 at 7:37 @mpiktas: you're right, good point. –onestop Feb 11 '11 at 8:51 3 @mpiktas, i usually explain the white noise to students through the spectral density concept, at least it gives light to (through the analogy with white color) why the noise is "white", and why the $AR(1)$ process could be could called "red" and there is no "black noise" :) –Dmitrij Celov Feb 14 '11 at 10:34 add a comment| up vote 8 down vote I myself usually think of white noise as an iid sequence with zero mean. At different times values of the process are then independent of each other, which is much stronger requirement than correlation zero. What is the best with this definition that it works in any context. Side note. I only explained my intuition, the correct definition of white noise is given by @onestop. The definition
noise is a random signal having equal intensity at different frequencies, giving it a constant power spectral density.[1] The term is used, white noise time series example with this or similar meanings, in many scientific and technical disciplines,
What Is White Noise
including physics, acoustic engineering, telecommunications, statistical forecasting, and many more. White noise refers to a statistical model for
Gaussian White Noise
signals and signal sources, rather than to any specific signal. A "white noise" image. In discrete time, white noise is a discrete signal whose samples are regarded as http://stats.stackexchange.com/questions/7070/what-is-a-white-noise-process a sequence of serially uncorrelated random variables with zero mean and finite variance; a single realization of white noise is a random shock. Depending on the context, one may also require that the samples be independent and have identical probability distribution (in other words i.i.d. is a simplest representative of the white noise). In particular, if each sample https://en.wikipedia.org/wiki/White_noise has a normal distribution with zero mean, the signal is said to be Gaussian white noise.[2] The samples of a white noise signal may be sequential in time, or arranged along one or more spatial dimensions. In digital image processing, the pixels of a white noise image are typically arranged in a rectangular grid, and are assumed to be independent random variables with uniform probability distribution over some interval. The concept can be defined also for signals spread over more complicated domains, such as a sphere or a torus. Some "white noise" sound. An infinite-bandwidth white noise signal is a purely theoretical construction. The bandwidth of white noise is limited in practice by the mechanism of noise generation, by the transmission medium and by finite observation capabilities. Thus, a random signal is considered "white noise" if it is observed to have a flat spectrum over the range of frequencies that is relevant to the context. For an audio signal, for example, the relevant range is the band of audible sound frequencies, betwe
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