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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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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18 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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10 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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21 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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12 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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18 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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10 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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46 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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45 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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6 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
40 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
17 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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35 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
33 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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27 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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1answer
54 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
14 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
51 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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20 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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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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24 views

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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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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1answer
55 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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1answer
18 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 ...
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4 views

Compute average pairwise correlation Y(X1) vs Y (X2) within many nonoverlapping intervals of variable X

I am pretty sure someone already solved this problem and shared the code. Could you please help to find it? I need to calculate the pairwise correlation for the values of a discrete function Y(X) ...
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autocorrelation interpretation (annual bird surveys)

I am following a method used by others (McCrimmon et al. 1997 Ecological Applications 7(2):581-592) to look for trends in the annual count of nesting pairs of birds at 29 nest sites over a 42 year ...
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31 views

What is the significance of autocorrelation?

Say that I have a signal that is strongly or weakly autocorrelated with itself. So what? What does this mean? How can this improve businesses? Does this mean that we can construct predictive models ...
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1answer
13 views

how does the MA lib determine the levels for what is significant or not for ACF

I am going thru this stats course https://onlinecourses.science.psu.edu/stat510/node/48 I can follow all the steps, but have question how the lib figures out what is significant for ACF. See "ACF for ...
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41 views

What is the point of lag plots and autocorrelation plots?

Most people seem to argue that lag plots and autocorrelation plots are useful for determining whether some univariate time series data is random or not. I feel like I could accomplish this task by ...
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PACF MA(1) via correlation of prediction errors

It is known (see e.g., Brockwell and Davis, Introduction to Time Series and Forecasting, p. 95) that the $h$th partial autocorrelation $\phi_{hh}$ of a stationary process can be derived by first ...
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1answer
51 views

What to do if ACF or PACF show significant higher lags?

I have monthly climate data for 90 years. I assembled the best model I could (added sensible parameters to minimize AIC), and then tried various ARMA correlation structures (using ...
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32 views

Interpreting ACF Plots

I need help interpreting this ACF plot. It was produced on R, where the function acf(ammns) was applied. "ammns" is the annual maxima of rainfall extracted from a dataset of monthly total rainfalls, ...
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11 views

Autocorrelation function for continuos observations

In the case of discrete observations (where the observations are made at constant time steps) it is easy with most packages to call an acf function such as ...
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24 views

How can I analyze trends in longitudinal NON-panel data?

I want to analyze data from the General Social Survey. The data is longitudinal individual level data but it is not panel data (yes, I know there's a recent implementation of a panel component - I'm ...
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1answer
76 views

Interpreting Ljung -Box test results from statsmodels.stats.diagnostic.acorr_ljungbox function (python)

I have a set of daily trading strategy returns and I am trying to prove whether the daily returns are autocorrelated at all. I am hoping to fail to reject the null hypothesis that they are not ...
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23 views

Conflicting results: Bartlett's periodogram-based test for white noise vs. Portmanteau test

When checking residuals of a fitted ARMA(1,3) model for the purpose of detecting GARCH effects in Stata (residuals uncorrelated, squared residuals correlated), I yielded conflicting results for the ...
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13 views

How can I test for seasonality with autocorrelation on a 100+ Poisson distributions (without graphs)?

I want to test Poisson distributions on seasonality by autocorrelation (without graphs, I want to calculate the LCL and UCL and program to test which autocorrelation lags exceed this). Now I know ...
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29 views

Which test for autocorrelation in a time series

I need your help to test autocorrelation between residuals of a time series. But I don't know which test use: Breusch Godfrey test, ARCH test or Durbin–Watson test.. I don't understand the difference ...
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54 views

Seasonality tests

I have data which I need to check for seasonality. Now I found two methods to do this, the autocorrelation plot and the rank Von Neumann ratio. Now I found the autocorrelation has some requirements: ...
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How many lags do I use for a VEC model with 4 endogenous variables for Residual Analysis?

I have 4 endogenous variables with 120 observations each. I would want to test for Autocorrelation using Portmanteau Test and LM-Type Test, for ARCH Effects using Multivariate ARCH LM Test, and for ...
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15 views

Derivation of the third moment of the count joint statistic

Does anyone know where I can find the derivation of the third moment of the joint count statistic? I found this similar question answered in the past: need derivation of join-count variance (spatial ...
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28 views

Durbin - Watson test for non Gaussian error terms

I am conducting time series regression on a large-sample data set. I would like to test for autocorrelation in the error terms. I have conducted the Durbin Watson test which tests for an AR(1) model ...
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12 views

How to compute and plot autocorrelation from MCMC [duplicate]

I'm learning about MCMC methods and following an example https://darrenjw.wordpress.com/2010/08/15/metropolis-hastings-mcmc-algorithms/ written in R that I ...