Autocorrelation is the correlation of a series of data with itself at some lag. This is an important topic particularly in the analysis of time-series data.

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How to calculate first order autocovariance in AR(1) process?

For a process describing dividend yield $x_t$, it is assumed to follow a first-order autoregressive process: $ x_t=\delta +\phi x_{t-1} + \eta_t $ where $|\phi|<1$ and $\eta \sim \mathcal{N}(0,\...
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Comparing differences between two groups while controlling for serial correlation

I would like to test for a significant difference between two samples of unequal size (sample size might differ by a factor of 5 or more), where the values within both samples exhibit serial ...
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11 views

Autocorrelation of coefficients for strongly autocorrelated inputs?

In Chapter 5 of "The Elements of Statistical Learning" ("Basis Expansion and Regularization", pg 150"), it is written that Since the input signals have fairly strong positive autocorrelation, ...
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12 views

Trend or stationary data [on hold]

I would to ask about acf data pattern that has shown from minitab output. Can I determine that the data pattern has trend? I'm still confused about how many lag should be a criteria for trend or ...
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15 views

How to reduce the residuals by autocorrelation of residuals?

I have two long matrix with Observations and Predictions, with 76 columns each. I need to reduce the residuals by means of autocorrelation of error correction. I also would like to select the best ...
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33 views

predicting the future in a stationary stochastic process

Let's say I have a strictly-stationary stochastic process with known PSD (power spectral density). The process has been running, and I have all the data from time $t=-\infty$ to $t=0$. I want to ...
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20 views

Autocorrelation specification in lme )

I am modeling wood properties variation of several individual within the same tree species using multilevel lme(). I specified a first model as : ...
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17 views

Logistic regression with temporal autocorrelated data

My objective is to simulate daily temporal series of wet/dry sequence of 2 years (730 days). I'm using a logistic regression with one continuous covariate, $x_{i}$, which is the rain amount of the day ...
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34 views

What is the PAC function of an AR(2)?

What is the PACF(1) of the following AR(2) process? $ y_t = \phi y_{t-2}+\epsilon_t $ with $\epsilon_t \sim WN(0, \sigma^2)$
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28 views

What does it mean that a variogram keeps increasing with distance?

I am modeling my 3D dataset with a Gaussian Process with square-exponential covariance. To test whether this is a good model, I subtract the mean from the observed data and then calculate the ...
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16 views

Auto-correlation Assumption

I am testing the auto-correlation assumption of OLS. My study is conducted on the most active companies on the Egyptian stock exchange over a period of 5 years. Not all companies included in the ...
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11 views

Correlation of Error terms v/s Auto Correlation

Is Correlation of Error terms and Auto Correlation same thing ? On page 93 of Statistical Learning the author describe the correlation of error terms but didn't describe how to check for correaltion ...
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24 views

How to apply linear regression to one sensor so that it will match readings from better sensor? [closed]

I have one sensor which has the best accuracy and the other sensor which I want to calibrate using some linear regression (or something else?) - by modifying the software. How to calculate that linear ...
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13 views

Breusch-Godfrey serial correlation test

I get an F-stat (with an F p-value) and an observations*R-squared (with chi-squared p-value) But I don't know which to use when reporting my results. When doing a hypothesis test, should I be using ...
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14 views

Correlation between sequential binary choices

I have an experiment in which subjects perform a binary choice for each question. I want to explore the effect of n-1 choice on the nth choice. I think it has something to do with autocorrelation but ...
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1answer
16 views

Simulating data with long range dependencies

I want to evaluate how well a recurrent neural network I've created captures long-range dependencies, and the effects altering the network have on this. I'm not entirely sure how I would go about ...
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33 views

Toda-Yamamoto procedure, testing autocorrelation in model residuals

I have been following the example given by Dave Giles blog post "Testing for Granger Causality". In the example lag length criterion suggests the lag length of 3. I constructed a VAR model with 3 lags ...
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1answer
44 views

Multiple regression with autocorrelated errors

I have a multiple regression model in R: ...
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1answer
44 views

What is causing autocorrelation in MCMC sampler?

When running a Bayesian analysis, one thing to check is the autocorrelation of the MCMC samples. But I don't understand what is causing this autocorrelation. Here, they are saying that High ...
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1answer
43 views

Ljung-Box test for ARMA residuals: is my ARMA model fine?

I have an ARMA($p$,$q$) model. $p=q=2$ gave me the lowest BIC value, and hence I stuck to it. I know people do something with the Ljung-Box $Q$-test test for autocorrelations. I did this on Matlab ...
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Incorporating shifting spatial autocorrelation into a GLMM

So I'm examining a series of sites across a landscape for how wildlife use of these sites changes following treatment (reclamation). Treatment of these sites randomly took place over three years, and ...
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71 views

How is the confidence interval calculated for the ACF function?

For example, in R if you call the acf() function it plots a correlogram by default, and draws a 95% confidence interval. Looking at the code, if you call ...
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64 views

VAR model selection, auto-correlation specification issues

I am encountering the following problems and I don't really know which model a should pick. All model selection criteria indicate that I should take the model with 1 lag. After building the VAR(1)-...
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1answer
60 views

Autocorrelated residuals from `auto.arima`

I'm having issues with the residuals of my ARIMA models in R for two time series. When I run the Ljung-Box test on the residuals, I get that I should reject the null (i.e. my residuals still have some ...
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16 views

Is this following assumption of autocorrelation test right?

Basically I ran an autocorrelation test using first the d-watson test which resulted in an inconclusive result as it equaled du stat. Then I ran the durbin-watson alternative test which resulted in ...
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Method for Estimating Autocorrelation in Severely Gappy Data

My question is somewhat long and boils down to "Does the following work?" I'm working on a project that involves timing analysis of astrophysical data sets that have large chunks of data missing due ...
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33 views

Optimal block length for block bootstrap with multivariate time series

I've got a multivariate time series $\mathbf{X}_t$, where $t$ is time and there are $p>1$ columns of $\mathbf{X}_t$. There is autocorrelation in the data. I'm interested in various functions of $\...
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Analyzing series of events, controlling lengths

(Excuse me for terminological problems. After I tried to find the solution, I started looking for at least the right names for the concepts I use, but I failed, as the simple descriptions I tried to ...
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53 views

Breusch–Godfrey test under heteroskedasticity

Do I need to account for heteroskedasticity when performing the (vector) AR1-2 test? The Autocorrelation (AR) 1-2 test is defined as follows - often reffered to as the Breusch–Godfrey test (Wiki link)...
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16 views

How to control serially correlated independent variables?

I'm interested in studying the impact of one variable (e.g., R&D expense at year T) on future firm performance (e.g., Sales in year T+5), I know it's incorrect to specify the following model: ...
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37 views

Heteroscedasticity,Autocorrelation,Chow test

Can a Chow test be run on a dataset which has autocorrelation and/or heteroscedasticity? Will the F-stat give accurate results?
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27 views

What do you think of this correlogram?

do you think this weekly data is stationary? Unit-root test indicates rejects null of non-stationary (rejects null of unit root). Thanks for your input.
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11 views

Testing for spatial autocorrelation in residuals - time series

I have a ~25 year dataset of annual count of species abundance in several traps. Within a year, the abundance in a trap might be dependent on the abundance in another trap. I want to test the effect ...
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274 views

How would I interpret this correlogram from EViews?

This is a correlogram on stock market data generated in EViews. How would I interpret it, in regards to AR and MA? Also, why are all my p-values 0? I would assume they wouldn't be as stock markets ...
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49 views

Incorporating autocorrelation into forecasts

I have a time series $x_{t}$ which is an AR(1) process with a constant term, e.g. $ x_{t} = c + \phi x_{t-1} + \epsilon_{t} $ How can I incorporate information about the autocorrelation of $x_{t}$ ...
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10 views

Using Mantel test to check spatial independence in time series?

For my analysis in biology, I want to study the effects of several factors (climate, cultivated area...) on insect dynamics and phenology. For that, I have data of insect captures from several traps ...
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1answer
45 views

Does autocorrelation imply stationarity?

Let $$ \begin{aligned} y_t &= a + bx_t + u_t, \\ u_t &= \phi u_{t-1} + e_t \end{aligned} $$ where $ e_t$ follows a White Noise process. Let Breusch-Godfrey LM test statistic be strictly ...
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Checking spatial autocorrelation by plotting residuals?

For my analysis in biology, I want to study the effects of several factors (climate, cultivated area...) on insect dynamics and phenology. For that, I have data of insect captures from several traps ...
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9 views

How to read the acf plot? [duplicate]

Please advise how to read the acf plot? How to interpret the dotted line? How to estimate the percent of confidence interval? Please feel free to advise. Thank you. ...
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1answer
27 views

Autocorrelation of VAR residuals

I am fitting a VAR model on 50+ timeseries that both have two variables, x and y. I am trying to identify if my bivariate VAR model has sufficient amount of lags. AIC nad SBIC both suggest using 2 ...
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43 views

Does ARMAX solve the autocorrelated errors and avoid spurious regression?

I have a OLS model looks like this: However, the residuals have auto-correlation like this: It doesn't seem a strong autocorrelation, and the model passes the Engle-Granger cointegration test (...
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54 views

Model residuals pass stationarity test, but Durbin–Watson test fails

I have a OLS model that I try to prove it has cointegration between two regressors and the dependent variable. The model fits well, with a very high R-squared. The residuals don't seem to be ...
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34 views

Help discussing stationarity using correlograms? ARMA/ARIMA modelling

I am currently trying to understand how to use correlograms to examine stationarity and analysis the appropriate models. Please can you advice, below I have included my ACFs and PACFs, and I am trying ...
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100 views

How to create a random walk model using {forecast} R package

I have a good understanding of ARIMA models but I've always found significant spikes in ACFs and PACFs that gave me the appropriate AR and MA parameters. Now I'm dealing with a series that is more ...
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18 views

difference between acf() from {stats} and Acf() from {forecast}

When I execute both functions on the same vector, I get slightly different graphs. I think I know what is happening but I want to confirm. acf() shows the spike at lag 0 which is 1 naturally, this ...
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1answer
74 views

Example of OLS vs GLS with AR1 residuals for teaching in R

I'm looking for an example to show my class. We are covering OLS vs GLS with autocorrelated errors -- I've got the class to the point where they understand (some of them) why the the standard errors ...
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23 views

Lag length for the Ljung-Box test

I have an ARIMA model applied on hourly data: Arima.fit2 <- Arima(tsTrain, order=c(17,1,0)) The length of my training set is 60 hours. In the end I plan to ...
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26 views

Autocorrelation test in case of heteroskedasticity and endogeneity

During my thesis I encountered the problem of having some degree of heteroscedasticity in my error terms. This creates a problem when I want to test for autocorrelation since for example the Breusch-...
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26 views

Simulation of time series from pdf function, defined for each time step, with aucorrelation

I have a model defined by $\mathbf{X}= (X_{1}, X_{2},... X_{t} ... X_{M})$, where for each $t$ (time step) $X_{t}$ follow a distribution ${D(\alpha_{t}, \beta_{t} )}$. I want to generate time series ...