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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1answer
2k views

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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3answers
6k views

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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1answer
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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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47 views

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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2answers
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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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1answer
607 views

ARMA models and invertibility

I'm reading the book Time Series Models by Franses et al. It says that if we have an $ARMA(1,1)$ model with $\phi=1$ and $\theta=-1$ we have $y_t=\epsilon_t$. So, this means that in the equation $(1-L)...
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1answer
769 views

How to estimate mean and standard deviation of a normal distribution from noisy data?

I have $n$ observations, $x_i$ following a normal distribution. I would like to estimate $\mu$ and $\sigma$ from my samples. Normally I would simply estimate $\mu=(\sum x_i)/n$ and $\sigma^2=\sum (...
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1answer
365 views

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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3answers
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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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1answer
724 views

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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1answer
341 views

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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1answer
19k views

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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1answer
5k views

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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2answers
95 views

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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1answer
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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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1answer
1k views

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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2answers
1k views

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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0answers
1k views

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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888 views

Confusion related to adding noise to a gaussian data

I have this confusion related to two methods to add gaussian white noise to data. Suppose I have a bivariate gaussian distribution with mean vector and covariance matrix $$ \mu = \begin{pmatrix} 0 \\...
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319 views

Estimating the autocorrelation function with some noisy observations

I am wondering how to estimate the actual correlation function when I have some noisy samples of some space. Lets say, I have a space and the locations in the space are variables following a ...
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2answers
3k views

Predictions of a monthly temperature time series: adding noise to the predicted values

I am doing predictions on monthly temperature data for 100 years, from 1901 to 2000 (i.e 1200 data points). I want to know if the method I follow is correct because in my output, I do not see the ...
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1answer
105 views

How to correctly model noise?

Assume a linear mixing model $x = As$, where $x = (x_{0}, ..., x_{n})^T$ are linear mixtures of $s = (s_{0}, ..., s_{n})^T$, and $A$ is the mixing matrix. Now, if I introduce additive noise to this ...
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1answer
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Why is it called white noise? [closed]

I know, that the white noise is called "white noise", because it comes from physics and has something to do with the spectral decomposition (is that right?) of the white light? I am not familiar with ...
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539 views

Pre-whitening of AR(2) time series

I'm working on a time-series problem. Consider the model below: $$Y = \beta_0 + \beta_1*t + \beta_2 * \sin(wt) + \beta_3 * \cos(wt) + \epsilon$$ For now, assume that $\epsilon$ is AR(2) with KNOWN ...
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2answers
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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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0answers
510 views

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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967 views

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 ...
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0answers
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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2answers
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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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2answers
1k views

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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1answer
50 views

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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2answers
5k views

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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2answers
2k views

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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0answers
149 views

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 ...
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1answer
95 views

Is there a classification of physical measurements according to their statistical distribution?

I am looking for a document or research articles classifying physical or chemical measurements (or perhaps better means of measurement) according to the reference statistical distribution and ...
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2answers
13k views

Formal statistical test for whether a process is a white noise

Is there a formal statistical test to test if process is a white noise?

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