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
1
vote
1answer
62 views

White noise assumption in the autocorrelation proof

I followed the proof presented in Quantitative Risk Management: Concepts, Techniques and Tools by D. Duffie, S. Schaefer (proposition 4.9, pages 128-129). To arrive at the numerator for the ...
3
votes
0answers
46 views

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 ...
1
vote
2answers
88 views

Probability density function for white Gaussian noise

in many signal processing text books and lectures we find that if we assume that the noise is white Gaussian then the probability density function itself takes the Gaussian form (see here for example) ...
1
vote
0answers
12 views

Applying fitted model of input on output time-series in pre-whitening

I have two different time series (input time series and output time series)for doing cross correlation. When I fit input time series for pre-whitening, it has good fit for ARIMA(0,1,1). So for pre-...
1
vote
1answer
34 views

Ljung-Box test to determine white noise of time-series (not residual)

I know we use Ljung-Box test to determine if the residuals are white noise or not. Can we use same test to determine if the time-series in itself is white - noise? This is to by-pass acf-pacf plotting,...
0
votes
1answer
23 views

Show that $x_{t},y_{t}$ are jointly stationary, and interpretation of CAcovF, $\gamma_{XY}(h)$ not being symmetric for lags $h$

Consider two white noise processes $(w_{t})_{t}$~$WN(0,\sigma_{w}^{2})$ and $(u_{t})_{t}$~$WN(0,\sigma_{u}^{2})$ that are also independent of each other such that $y_{t}=w_{t}-\theta w_{t-1}+u_{t}$ ...
1
vote
1answer
26 views

Second-order moments of a White Noise process

One of my textbooks on time-series analysis claims that Dependency in the second moments of the residuals contradicts the assumption of a constant, time-invariant variance. Thus [the residual] is not ...
0
votes
0answers
21 views

Probability of periodic signal in gaussian white noise time series

Suppose I have time series data that is accurately modeled as gaussian white noise with mean and variance $\mu, \sigma^2$. I would like to write down a probability density characterizing the ...
0
votes
1answer
53 views

Math behind Differencing: Is White Noise Stationary?

I'm just starting to learn the math behind stationarity and differencing, so I apologize if this is a silly question. Lets say I have a non-stationary time series process (pure random walk) defined by:...
2
votes
1answer
28 views

Vector AR/ARMA Model [closed]

For a vector AR/ARMA model in practice, if there are k different time series in the vector, there are k corresponding Gaussian white noises as well. Is it realistic to assume that those k white noises ...
0
votes
2answers
166 views

Is an independent process always a white noise process?

In econometrics, an independent process means that all values are independent of each other, but does this also mean that all independent processes are white noise processes? and is the reverse true?
0
votes
1answer
36 views

Variance of a white noise process

How do I find the variance of this? $$y_t=M + \sum_{i=0}^n 0.5^i\varepsilon_{t-2i}$$ M is the mean.
0
votes
0answers
4 views

ljung box test for space time model

i did white noise test using ljung-box for space time model. i used mq function but the output always change everytime i running. is it really like that? thank you library(MTS) wndb=matrix(rnorm(468),...
1
vote
2answers
75 views

Is error term in MA model in univariate time series the same as white noise

I what to know if the error term referred to in moving average model of time series the same as white noise? which is usually define in r as ...
1
vote
1answer
56 views

In a VAR model, why are white noises correlated with each other in the reduced form model

With my understanding, we have 2 different models when studying VAR processes (Vector Autoregression). We have $$ \begin{bmatrix} y_{t} \\ x_{t} \end{bmatrix} = \begin{bmatrix} c_{1,0} \\ c_{2,0} ...
1
vote
0answers
23 views

Interpreting Ljung-Box white-noise test p-value

Good evening all, I am having some trouble understanding the Ljung-Box white-noise test p-value from SAS Forecast. So there are lags where the p-value exceeds 0.05, meaning that we fail to reject the ...
0
votes
0answers
75 views

Is an ARIMA(0,0,0) with non-zero mean equivalent to white noise?

Is an ARIMA with a non-zero mean equivalent to white noise? If not, how should the mean be interpreted?
0
votes
0answers
56 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
118 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
51 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
50 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
7 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
73 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
272 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
696 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
184 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 ...
1
vote
1answer
88 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
47 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
147 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
41 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
133 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 \\ \...
1
vote
1answer
204 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
15 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
33 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 ...
2
votes
1answer
292 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
134 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
1answer
240 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
105 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
34 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
49 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 ...
5
votes
3answers
681 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 is summing up a bunch of white noises related to predicting your particular time series data? Suppose I have a MA(q) ...
1
vote
0answers
32 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
217 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
2k 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 ...
3
votes
1answer
559 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
120 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
526 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
67 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
86 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
339 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 ...