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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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Do coefficients in moving average process add to 1?

I'm studying weakly stationary stochastic processes, and I'm confused by the title of the "moving average" representation of such a process. Suppose that $y_t$ is a weakly stationary stochastic ...
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1answer
27 views

Parameters of ARMA model

In my professor's notes, it is written that if the variable $y$ is explained with an ARMA($p$,$q$) model, then $y_t$ (i.e. $y$ at time t) depends on the most recent $p$ lags of its own value and the ...
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does white noise residuals suggest a stationary model?

To fit an ARMA model to a time series, the time series should be stationary to start with. If we obtain a reasonable model fit by looking at mean and variance, ACF ...
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1answer
34 views

Understanding the infinite sum of random variables

I am doing a course on time series analysis, and am struggling with this definition: We call a weakly stationary process $\{X_t\}$ invertible with respect to a white noise $\{\epsilon_t\}$ if ...
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37 views

If the ACF of a time series is within the 95% bounds, is it white noise?

I have a detrended series where the ACF and PACF has lags all within the 95% confidence bounds. This would suggest the series is a White Noise. However, fitting it to an ARMA model (in R) gives the ...
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33 views

Test for white noise in time series: Bartlett vs Ljung Box test

I am modeling a time series data using ARIMA with regressors for monthly and weekly seasonality (Fourier term approach is very slow). I am using Hyndman's forecast package for modeling the data. My ...
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1answer
22 views

How to determine mse of estimate from correlation matrix of estimate error?

I have a model of an information transmission system Y = XH + N, where X is a diagonal matrix with the transmitted "symbols" (known), H is a column vector which distorts the transmitted symbols and N ...
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48 views

Can the sum of several time-series be a white noise process, when the individual time series are not?

Intuitively, I think that it is possible for a sum of time series to be white noise, when the individual time series are not. Reason I am asking, is because I want to know if it's useful to ...
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26 views

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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32 views

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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113 views

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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25 views

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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1answer
95 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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487 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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76 views

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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339 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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2answers
98 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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53 views

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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190 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
363 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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3answers
2k views

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 $\kappa$. ...
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255 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
58 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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72 views

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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1answer
328 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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1answer
70 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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1answer
2k 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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46 views

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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481 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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420 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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171 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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68 views

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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1answer
820 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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30 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
92 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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423 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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2answers
1k views

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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42 views

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
262 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
71 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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2answers
2k 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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846 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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1answer
442 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
356 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
609 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 "...