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 do I interpret ACF and PACF figures from a SARIMA model? [on hold]

I have data about tourism arrival. the plot of data is this is result after first differencing So, what is SARIMA model for this problem?
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32 views

autocorrelation plots interpretation

Q: How to interpret the following ACF plots (of residuals). Its monthly data : The black lines are the 95% confidence intervals. here is a plot of the residuals.
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16 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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12 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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10 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? [on hold]

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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9 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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12 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
10 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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25 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
41 views

Multiple regression with autocorrelated errors

I have a multiple regression model in R: ...
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1answer
39 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
27 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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1answer
53 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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14 views

Weighting of predictors in a temporally correlated mixed effect model

I want to investigate the impacts of historic factors (vegetation density) on biodiversity sampled in the present. These historic factors all very likely all temporally autocorrelated with each other. ...
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50 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 ...
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1answer
58 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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26 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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12 views

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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40 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 ...
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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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1answer
28 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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23 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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128 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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48 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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7 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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41 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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17 views

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
20 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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39 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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1answer
44 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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32 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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70 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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1answer
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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69 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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21 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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23 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 ...
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22 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 ...
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15 views

Serial Correlation & Bootstrapping

I just ran into an stats problem that is a bit esoteric. (1) I am implementing a method that bootstraps clustered standard errors. It does this due to having a a variable that is the predicted values ...
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Autocorrelation of concatenated independent AR(1) processes

Let $\left\{X_t\right\}$ be a stochastic process formed by concatenating iid draws from an AR(1) process, where each draw is a vector of length 10. In other words, $\left\{X_1, X_2, \ldots, ...
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14 views

Which approach to use for Spatial Autocorrelation, Moran's I?

I am working out with some spatial data from Yelp dataset. I'd like to take a single city, plot all the restaurants and then check wheter there's some clustering that affects the grade that people ...
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65 views

What to do if time series data remains autocorrelated?

Data: I have 92 years of monthly climate data. One of my variables is a drought index (SPEI) ranging from -2 (dry) to 2 (wet). All the data can be found here. Data Structure: ...
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19 views

Phase shifting a signal

I have a signal of the form $s(t)=A(t) \sum cos(\omega_i(t)t +\phi_0) + n(t)$, where $n$ is gaussian noise. Now I want to phase shift this to $A(t) \sum cos(\omega_i(t)t)$ and I am at a loss on how ...
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35 views

Bayesian Classification-High autocorrelated chain

I'm trying to make a bayesian prediction for categorical data using OpenBUGS,R and their interface package R2OpenBUGS. For this purpose, i'm fitting a categorical-logistic regression model between the ...