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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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Continuous white noise

I have been reading about topics that include statistics, and slowly start to get a grasp. However sometimes it seems to me that I dont get the simplest concepts. White noise seems to have several ...
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How to determine the line which a time-series fluctuating around

Let $X_t=1+3t+0.5X_{t-1}+ \epsilon_t$ be a trend-stationary model, where $\epsilon$ is a white noise, which has zero expected value and standard deviation. Which line is the time series fluctuating ...
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Where does the white noise come from in MA(q) model?

I'm having trouble understanding the intuition of the moving average model. How does summing up a bunch of white noises related to predicting your particular time series data? Suppose I have a MA(q) ...
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Using a neural network for a regression problem, where the model to be learned suffers from awgn

I have currently a neural network to learn a (relatively non complex) system model (vector regression). Its problem is that the outputs of the system suffer from arbitry additional white gaussian ...
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34 views

Mean and Correlation of a First-Order ARCH(1) Process

For a first-order ARCH(1) process $$ Y_t = \epsilon_t(\alpha_0 + \alpha_1Y_{t-1}^2)^{1/2} $$ $$ t \in \mathbb{Z} $$ $$ \alpha_0, \alpha_1 > 0 $$ $ \{\epsilon_t\}_{t \in \mathbb{Z}} $ and $Y_t$ is ...
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What determines whether relative or absolute Gaussian noise should be added to data?

Suppose I have some data vector, $\mathbf{d}$ with length $N$. I want to add "Gaussian noise" to the data. My understanding is that there are two ways to do this. 1) Relative noise percentage $$\...
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106 views

“Add White Gaussian Noise with SNR” vs. “Add 5% Gaussian Noise”

I have a noise-free dataset which is a vector of numbers, $\mathbf{d}$, with length $N$. I want to "add noise" to this data. My understanding is that there are two ways to do this. 1) Add some ...
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What's a discrete-value zero-mean distribution for modelling white noise? [closed]

For many settings one uses the normal distribution $\mathcal{N}(0,\sigma^2)$ to model the white noise (e.g. noise on a communication channel). What's a similar discrete-valued version of this that is ...
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111 views

How to Interpret these ACF/PACF plots

Would it be safe to regard this time series data as a white noise? Here's the dataset I used for computing the ACF/PACF Date 2008-05-23 0.323555 2008-10-15 0.650817 2009-03-11 -0.193327 ...
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Correcting for noise in gene expression data

I have a training set of RT-qPCR gene expression data (not run in triplicate) for a batch of samples with two phenotypes $A$ and $B$ on which I've trained a logistic regression classifier. I also ...
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77 views

ARMA models and residual series

Assuming that model is correct, why does the residual series of an ARMA model resemble a white noise process?
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Covariance Functions of Stationary Gaussian Random Processes

I am trying to solve this question: Suppose that $n(t)$, $−∞ < t < ∞$ is a stationary Gaussian random process with covariance function $E\{n(t)n(t-\tau)\} = \delta(\tau) + {5 \over 4}e^{-\left|\...
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Least Squares fit of model - R

The data file (X in code thread below) contains the record of monthly data X[t] over a twenty year period. The data can be modelled by X[12j+i] = Mu + s[i] + Y[12j+i] where (i=1,...,12; j=1,...,k) ...
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159 views

Create Gaussian noise for artificial dataset with different noise levels

I am creating an artificial dataset corresponding to different noise levels. This is to simulate results of a recognition software (e.g. face recognition). For example, for $noise_{level} = 0.1$, the ...
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1answer
254 views

Why is the variance of ACF of white noise 1/T

In many books, articles and comments on this website I read that the variance of the autocorrelation of a white noise process is $\frac{1}{T}$ when T is sufficiently large. Often this characteristic ...
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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 depned only upon the time difference $\kappa$. ...
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346 views

Sigma in Arima Models Stata Output

In stata, after running an arima regression model, how should I interpret the last line 'sigma'. I understand that sigma is referring to the standard deviation of the error term, but how should it ...
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206 views

White noise test taking into account homoscedasticity

I try to test a time series for white noise. The ultimate goal is to show that scaling volatility from daily to longer time periods by the square-root of time rule is justified. Fore white noise I ...
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1answer
52 views

Choosing right Model exchange rate

I have obtained these two plots using R, I have to fit a model and the trouble is choosing between an ARMA(0,0), and an AR3. The main issue is the autocorrelation at lag 3, is it enough significant to ...
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Is there any white noise test that tests whether its variance is equal to a certain value $\sigma^2$ or not?

To my knowledge, all white noise tests are to test whether a process is a white noise or not. Is there any test in time or frequency domain, that test for a white noise, whether its variance is equal ...
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23 views

Full frequency space description of a continuous-time random process (e.g. signal) in

I don't know if signal processing or math would be a better forum, but I'll start here. Consider an ensemble of stationary random processes $x(t)$ that has the following properties: The PDF is $P[x]$...
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164 views

Interpretation of an I(2) process?

I know that an ARIMA(0,0,0) process is white noise and ARIMA(0,1,0) is a random walk, Is there an interpretation of what an ARIMA(0,2,0) process is?
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51 views

Finding a suitable distribution for a data set of white noise

In the plot we see a mean zero process. It not entirely normally distributed. How can I find a suitable distribution for this process? It needs to be white noise and hence iid.
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1k views

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 ...
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If $Y_t$ is not white noise, why $X_t$ can't be Normal?

Let $\{X_t\}$ be an white noise process and $\{Y_t\}$ a second process where $Y_t=X_t^2$. If $Y_t$ is not white noise, why you can say that $X_t$ don't have Normal distribution? I can not see the ...
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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 $WN(0,σ^2)$...
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352 views

What is the meaning of white noise in AR model?

I am new to Time Series. I want to know the meaning of white noise. By definition it is given that $w_t\stackrel{_{_\text{iid}}}{\sim} N(0,σ^2_w)$, meaning that the errors are independently ...
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Who says trading data are noisy?

We try to denoise our time-series and model inputs with a plethora of methods like Kalman filters, EMA, Kernel filters, Splines, Beziers, etc. But who came up with a theory that trading data is noisy ...
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342 views

Variance of white noise in time series models

I have a time series of 2400 observations and fitted some different time series models (AR(6), MA(35), ARMA(6,1), etc.). Every model has a residual $e_t$ which is white noise with mean=0 and a ...
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115 views

Do Principal Component Analysis regression eliminate noise in the data set?

I am comparing the perfomance of PCA regression (i.e. regression where original regressors are replaced by few their pr. components) to that of regression with the original regressors in which I added ...
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Simultaneously whitening correlated vectors

I have a $P \times K$ matrix $\mathbf{Z} = \begin{bmatrix}\mathbf{z_1} & \mathbf{z_1} & \cdots & \mathbf{z_K}\end{bmatrix}$. I want to whiten the columns of $\mathbf{Z}$ so that the ...
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572 views

Is it necessary for white noise to have zero mean

Where ever we see in the text books authors explicitly mentions zero mean white Gaussian noise and in practice also noise processes are zero mean.But if some process is Wide sense stationary but non ...
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28 views

What tests do I need to run to conclude that I cannot use ARIMA for a series?

I am trying to fit an ARMA model to a stationary series. Following the methodology from a paper I regress my data on a constant and look at the Q-stat for lagged value to check if there is serial ...
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1answer
80 views

Spectral density of square of AWGN

Additive white Gaussian noise (AWGN), $w(t)$, is usually modeled with the following assumptions For a given $t_0$, $w(t_0)$ follows a normal distribution and $R_{ww} = \sigma^2 \delta(t)$, where $\...
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350 views

Estimating the white noise of a Random Walk

I want to simulate a random walk without drift to predict a time serie. The random walk model is $X_t = X_{t-1} + \epsilon_t$ where $\epsilon_t$ a white noise with a Normal distribution. It seems ...
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Does a white noise process have constant variance by definition?

If you'll look up for the definition of a (discrete) white noise process on the web, you'll find some sources that say: "white noise is defined by zero mean, finite and constant variance, zero ...
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Signal to Noise Ratio of a train of pulses

My signal was a train of rectangular pulses consisted of eight pulses with interval between pulses of 36 s with a temporal resolution of 0.1 s. I added a Gaussian noise oscillations with zero mean and ...
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1answer
222 views

Infinite variance for a discrete-time white noise process

In a variety of contributions (e.g. Wikipedia) it seems that an infinite variance is linked (as a theoretical limit) only with continuos-time white noise processes. However, in some papers/notes an ...
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1answer
64 views

Why is the $E(y_{t-1}\epsilon_{t-1})=\sigma^2$?

I am trying to understand how to derive the ACF and PACF of and ARMA(1,1) process. In one of my lectures I have the following ARMA(1,1)$$y_t=\phi y_{t-1}-\theta \epsilon_{t-1}+\epsilon_t$$ I am being ...
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1k views

Why white noise process and IID process are considered martingale [closed]

Can anyone explain to me why A white noise process (εt) and An IID process (εt) are martingales?
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678 views

Can white noise be removed using moving averages?

In the book Time Series Analysis by R, the author mentions the use of moving average to smooth out the white noise. Can moving averages be used to remove white noise or are there better methods?
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353 views

Generating Error Vectors (White Noise) for Simulation of Vector Autoregressive Model (VAR)

I just estimated a Vector Autoregressive Model with 6 lags and 10 variables in R. My goal is to simulate the given original time series (on which the model parameters were estimated) to see how the ...
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1answer
290 views

White noise residuals but not fits as normal distribution

I'm having problems with forecast and SARIMA. Got successfull estimation when looking to white noise residuals, but they don't fit as a normal distribution. ...
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1answer
497 views

Can white noise be (losslessly) compressed?

Can I expect a vector whose components are i.i.d. Gaussian noise to be compressible (lossless compression)? Why or why not? If so, how much? EDIT: To be clear, I mean "compressible" as in "...
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266 views

Categorical white noise

Categorical time series such the genomic DNA, the sleep state of a person $\cdots$ etc, are often treated and analyzed. The first question that came to my head was how can such type of series be a ...
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444 views

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 ...
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1answer
544 views

The ARIMA(1,1,2) model for log(dataset) seem insignificant compare with ARIMA(1,0,2) model for diff(log(dataset))

I am trying to fit ARIMA model for my dataset. I did the following steps: Here is my dataset plot and log plot after log transformation (...
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94 views

Model-based Bayesian inference with unknown noise variance

I want to infer the conditional posterior distribution of the unknown system parameter $\theta_1$ given the empirical data $\boldsymbol{y}$, with $\theta_1 \in \mathbb{R}$ and $\boldsymbol{y} \in \...
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2answers
1k views

How to prewhiten univariate time series?

This is what I have tried so far ...
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285 views

Residual diagnostic correlogram q statistics

I am trying to get information from the correlogram of residuals in eviews from a certain equation. And it is stated that the p-values should be all greater than 0.05. But all of my p Values are ...