Statistical Analysis Stack Exchange
Statistical Analysis Stack Exchange

Questions tagged [white-noise]

White noise is a random process whose "components each have a probability distribution with zero mean and finite variance, and are statistically independent".

White noise is a random process whose "components each have a probability distribution with zero mean and finite variance, and are statistically independent" (Wikipedia). When white noise is distributed like a normal distribution it is called Gaussian white noise.

In statistics and econometrics one often assumes that an observed series of data values is the sum of a series of values generated by a deterministic linear process, depending on certain independent (explanatory) variables, and on a series of random noise values. Statistical model validity of standard time series models often depends on the assumption, and it is routinely assessed (via Ljung-Box, Breusch-Godfrey, ARCH-LM and other tests) in model evaluation.

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White Noise in Statistics

I often see the term white noise appearing when reading about different statistical models. I must however admit, that I am not completely sure what this means. It is usually abbreviated as $WN(0,σ^2)$. Does that mean it's normally distributed or…
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Is the sum of two white noise processes necessarily a white noise?

Let $a_t$ and $b_t$ be white noise processes. Can we say $c_t=a_t+b_t$ is necessarily a white noise process?
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How is adding noise to training data equivalent to regularization?

I've noticed that some people argue that adding noise to training data equivalent to regularizing our predictor parameters. How is this the case? Some of the examples listed on SE discussing this topic focus more on e.g. LSTMs and SVMs, but can we…
Ice Tea
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Formal statistical test for whether a process is a white noise

Is there a formal statistical test to test if process is a white noise?
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Testing normality and independence of time series residuals

The simplest form of a white noise process is where its observations are uncorrelated. We can check this by applying e.g. a portmanteau test such as Lung - Box or Box - Pierce. The series might be Gaussian white noise where the observations are…
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How to generate uncorrelated white noise sequence in R without using arima.sim?

I want to know how to generate uncorrelated white noise sequence $WN(0,\sigma^2)$ in R **without using ** arima.sim(list(order=c(0,0,0)),200) ? The reason I post this in here instead of stackoverflow is because I feel like this requires…
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How to prove that the Fourier Transform of white noise is flat?

If we take $X_n$ a series a random vector with its components each having a probability distribution with zero mean and finite variance, and are statistically independent. How do we prove that the power spectrum of $X_n$ is flat?
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Box-Ljung test on white noise series

I generate this data in R: set.seed(111) ds=rnorm(1000) When I perform Box-Ljung test to test the independency: Box.test(ds,type='Ljung',lag=log(length(ds))) it gave me p-value=0.5957, which is reasonable. However, when I perform…
Elaine
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Is there a classification of physical measurements according to their statistical distribution?

I am looking for a document or research articles classifying physical or chemical measurements (or perhaps better means of measurement) according to the reference statistical distribution and properties they have. Example of questions studied would…
ogerard
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Why is it called white noise?

I know, that the white noise is called "white noise", because it comes from physics and has something to do with the spectral decomposition (is that right?) of the white light? I am not familiar with signal theory, so could anyone explain me why it…
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Does white noise imply wide-sense stationary?

White noise has the ACF: $R_{WW}[\kappa] = c_0 \delta [\kappa]$ and zero mean $m_W[\kappa] = 0$. The first and second order moments of a WSS process depend only upon the time difference $\kappa$. With that being said, since $m_W $ is always zero,…
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Determining whether a Time series is white noise

I have a time series of log-returns of a stock. I want to determine whether the time series is just white noise or if there are some other pattern. How to I use the definition of white noise to make a conclusion?
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Discrete white noise

I have a binary time series $\{X(n), n= 0,1,2,\cdots\}$, $X(n)\in \{0,1\}$ that can be written as: $$X(n)=S(n)+\epsilon(n)$$ Where $S(n)$ is a random stationary binary signal and $\epsilon(n)$ is a zero-mean binary white noise process (uncorrelated…
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Are colored noises correlated / uncorrelated?

Let, $x$ be a random variable (r.v) that is white Gaussian, has a flat power spectrum. $y$ can be any colored noise. I think another term for uncorrelated is i.i.d (identically and independently distributed). Colored noises such as pink, brown, and…
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Optimization of an objective function with noise

I want to estimate the parameters that minimize a multivariate function with noise based on realized observations. As a simple example, say I have observed the univariate sample below: The samples were generated from a quadratic function plus…
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