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".

Filter by
Sorted by
Tagged with
0
votes
0answers
34 views

Forecasting with ARIMA models

I want to do a rolling window forecast on a time series but it seems the series is white noise ARIMA (0,0,0) with non-zero mean. But when I difference the dataset and model it with an ARIMA(0,1,1) I ...
2
votes
1answer
29 views

What is the difference between white noise and “strict” white noise?

The normwhn.test package in R has a function to test if data is white noise. The documentation of the function states the following : Performs an Univariate Test ...
0
votes
1answer
21 views

Statsmodel Ljung-Box test for non-zero mean

I have few time series, which I would like to model using ARIMA. But plotting ACF and PACF indicates these series are probably white noise. I am using Ljung-Box test to confirm it. I am implementing ...
1
vote
1answer
20 views

In ARMA model, the white noise is uncorrelated, but why there are autocorrelation existing between them?

I learnt the ARMA model allows the autocorrelation between noise. but I check the definition of white noise is a sequence of uncorrelated, fixed mean random variables. how can the uncorrelated random ...
0
votes
0answers
6 views

Does the procedure of progressively adding noise have a name?

I want to make a qualitative estimate of the amount of noise in my dataset $X$. For that purpose, I use a certain information estimator $F(X)$ (for example, mutual information between two different ...
1
vote
1answer
33 views

Time Series assumptions for iid $\epsilon$

thanks for reading my post. I know its fundamental and rather easy qns but I'm seriously struggling. Please help me, thank you very much! Let $\boldsymbol{X}$ have a distribution with mean $\mu$ and ...
0
votes
1answer
62 views

Proof of white noise process

I have the process $y_t=e_t+ae_{t-1}e_{t-2}$ where $e_t$ is iid with mean of $0$ and variance $\sigma^2$ How do I go about mathematically proving that this is a white noise process?
0
votes
1answer
93 views

Autocovariance of White Noise

I'm studying time series, I don't understand the description below. The white noise series $w_t$ has $E(w_t) = 0$ and $$\gamma_w(s, t) = \operatorname{cov}(w_s, w_t)= \begin{cases} \sigma_w^2 & ...
0
votes
1answer
65 views

What is the relation between the serial correlation and white noise series?

I am a bit confused about why would I use the Ljung-Box test in order to determine whether a series is a white noise ? I know that the Ljung-Box test studies whether we have serial correlation. I ...
0
votes
0answers
33 views

Outliers Kalman Filtering

This might not be the right place to ask this questions, but I figured it's more of a machine learning question. I am also asking on the pyro forum for brevity. I'm working with the simple extended ...
0
votes
1answer
33 views

What happens when a time series is multiplied by an iid error

Let's say say I have a standard AR(1) process, apart from the fact that is multiplied by the $ε_i$~$iid (0,1)$. Would this affect the independence of the the AR(1) series? My intuition is no ...
0
votes
1answer
51 views

How to compute error terms in moving average time series model? [duplicate]

Currently I am studying time series Moving Average model MA(q) $$X_t -\mu= \epsilon_t + \theta_1\epsilon_{t-1} + \theta_2 \epsilon_{t-2} + ... + \theta_q \epsilon_q$$ where $\theta_1,...,\theta_q$ are ...
1
vote
1answer
29 views

Including regressors to improve forecasts on white noise

I am conducting some time series forecasts using quite limited data, 13 years annually. Basically, I am trying to forecast companies emission totals using historical values. The historical data ...
0
votes
0answers
49 views

Add Noise to a Dataset

I've generated a dataset of 100 elements from a 3-variate Gaussian distribution with parameters $\mu = 0$ and $\Sigma = \begin{pmatrix}1 & \rho_1 & \rho_2 \\ \rho_1 & 1 & \rho_1 \\ \...
0
votes
0answers
16 views

Relationship between L2-norm of the noisy observations

Assume $\mathbf X_1^n$ is a vector of size $n$ whose elements are either $+1$ or $-1$. Then, we define $$\mathbf Y^n=\mathbf X_1^n+\mathbf N^n$$ where $\mathbf N^n$ is Gaussian additive noise with ...
1
vote
1answer
111 views

Wold Decomposition Theorem and Moving Average model - Error Terms

I'm stuck with Wold's decomposition theorem in time series analysis. The theorem says that every stationary time series can be written as a sum of two components, one being entirely deterministic (...
0
votes
0answers
13 views

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 ...
2
votes
1answer
30 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 ...
0
votes
0answers
27 views

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 ...
2
votes
1answer
146 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 ...
1
vote
1answer
67 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 ...
0
votes
0answers
144 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 ...
0
votes
1answer
89 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 ...
2
votes
0answers
80 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 ...
0
votes
0answers
30 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 ...
0
votes
0answers
37 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 ...
2
votes
3answers
357 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) ...
1
vote
0answers
30 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 ...
2
votes
1answer
143 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 ...
0
votes
0answers
1k 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 ...
2
votes
1answer
456 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 ...
3
votes
0answers
119 views

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 ...
3
votes
2answers
201 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?
0
votes
0answers
61 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|\...
2
votes
0answers
83 views

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) ...
0
votes
0answers
255 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 ...
2
votes
1answer
524 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 ...
4
votes
3answers
4k 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 $\kappa$. ...
2
votes
1answer
301 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 ...
0
votes
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 ...
1
vote
0answers
83 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 ...
3
votes
1answer
519 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?
0
votes
1answer
109 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.
4
votes
1answer
4k 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 ...
2
votes
0answers
47 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 ...
29
votes
2answers
6k views

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 $WN(0,σ^2)$...
1
vote
0answers
614 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 ...
2
votes
0answers
87 views

Who says trading data are noisy? [closed]

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 ...
0
votes
0answers
238 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 ...
0
votes
0answers
88 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 ...