# 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".

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### ARIMA modeling white noise probabilities vs. residual autocorrelation/PACF

I have moderate understanding of statistics and time series analysis. I trying to forecast a weekly time series with lots of outliers and trend shifts. After correcting all of the outliers, I'm left ...
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### Correlogram q-statistics of residuals

I am currently try to get information from the correlogram of residuals in eviews from a certain equation; I am supposed to understand if residuals are white noise or not and to adfirm that they 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 ...
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### Can I say that residuals are white noise?

I want to check whether residuals are white noise or not. When I look at the plot, all lags do not pass(exceed) the significance band except for fourth lag. However, fourth lag's p-value of 0.228 is ...
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### the decision of being White noise on e-view

And for example, let's take SMA(2) model in this table does there exist white noise ? Which value I observe to decide the existance of white noise? Please explain it. Thank you
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### White noise ACF - PACF

I found PACF and ACF like the following table . But, how can I decide whether there exists white noise? And what is white noise? If there is no white noise, can I say being stationary?
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### Does the noise term in a SDE need to be Gaussian?

Most of the examples I've seen for stochastic differential equations are of the form: $$dX_t = \mu(X_t, t)dt + \sigma(X_t, t) dW_t$$ where $dW_t$ is a Wiener process, i.e., the independent ...
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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 ...
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### Whitening a regression with an AR process

I was reading a research paper: $Y_{t}\text{=}\beta_{0}+\beta_{1}X_{1t}+\beta_{2}X_{2t}$ (where $Y_{t}$ is stock returns and not the change in stock returns) ($X{}_{1t}$ is the return of a stock ...
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### Why do we prefer white noise and iid property?

EDIT When we add noise to system we say it is white noise. White noise will have a constant power spectral density, flat power spectrum. But what is the advantage of this? Why do we need iid property?...
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### Getting Residuals to be White Noise

I'm on a time series project for an undergraduate course. For the project I'm trying to come up with an ARIMA model for the housing starts data set. http://www.quandl.com/FRED/HOUST-Housing-Starts-...
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### Is ARMA(0,0) equivalent to white noise?

If the EACF of my TS suggests ARMA(0,0) and the Box-Ljung test does not suggest my TS has correlation, can I conclude that my TS is white noise or merely that there is no reason to suspect that it is ...
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### Estimation of unknown vector's amplitude with Gaussian noise

I have the following model: y = P v + n Where y is the vector of observations, v is a unit vector and n is a Gaussian random noise whose covariance matrix is the identity matrix. P is a positive ...
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### Recovering true data from many noisy samples with varying unknown amounts of noise

Input: $k$ vectors $x^1,\ldots,x^k \in \mathbb{R}^n$, where $x^i \sim \mathcal{N}(x,\mathbb{1} \cdot \sigma_i^2)$. Goal: approximate the vector $x$ as well as possible. The quality of approximation ...
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### Diagnostic for VAR model. non normal

I have some problem about my model. my model is based on VAR. (vector auto-.) well, I've tested ARCH test, BG test(autocorrelation p) and jarque.bera.test. Model is stable. Also I got good result for ...
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### Is this process an AR(1)?

The following process $X$ is generated as the sum of a structure $y$ and an $AR(1)$ process with $\phi=0.4$ and $\sigma_{\epsilon}^2=1$: ...
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### Strange results of Ljung-Box test (for white noise process)

Ljung Box test tells that the following time series is white noise (p=0.9746845 for the current run). How could this be? ...
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### Estimating noise variance

I want to know how can we estimate the noise variance from noisy observations. Lets say. I have a variable x that has mean u and variance $\sigma^2$. Now lets say I have 100 samples of this variables. ...
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### Random walk with drift are differences white noise?

If I have a random walk without drift the differences form a white noise process. But what happens if I incorporate a drift $d$? Does this still hold true? I'm not sure because with the drift term d: ...
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### Classification accuracy is better with noise added?

I'm making a system to classify 2 class motor-imagery EEG of human brain. I use simple Low Pass Filter to pre-process the data (with or without added noise). I'm using LDA as my classifier. To test ...
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### White noise for level, log and log differences data sets

I am using eviews 7 and I have 3 data sets for DAX stock market index: level (dax), log (ldax), and log differences (dldax). I need to check whether the error terms of these data sets are white noise ...
834 views

### Statistical test for whether a process is a red noise

We know that red noise is the same as a ﬁrst-order autoregressive (AR(1)) stationary Gaussian process with a positive correlation at unit lag. Does there exist some formal statistical test for red ...
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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: ...
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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 ...
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### Noise correlations depending on distance

If one has noise being generated over time $t\in[a,b]$, and the correlations of the value of the noise at times $t_0$ and $t_1$ turn out to be distributed according to a density function that depends ...
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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 ...
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### Why does noisy data result in better prediction performance?

I have tested a regression framework's robustness to noise and I have noticed in some cases that adding noise improves the prediction performance and in other cases the performance degrades. What ...
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### Determing noise type and level of noise

Context I have a set of data that was collected from several inertial measurement units (orientation and acceleration data). I want to determine to what extent an inference method degrades when the ...