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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Autocorrelation or Serial Correlation

Autocorrelation is also known as serial correlation . Why is the terminology serial used ? Is there anything unserial or ...
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Compare sample means of normal distribution with autocorrelation issues

Please forgive me if this is a naive question, but I haven't been able to find an answer in my stats books or online. I'm working on a fish tracking dataset that consists of detections of tagged fish ...
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51 views

Difference between different autoregressive models

I am trying to understand the difference between these three different specifications of an autoregressive model for variable var in Stata: ...
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Fitting a time series model to potentially seasonal data

I'm analyzing a data set that appears to be seasonal but I can't figure out the appropriate model. I made ACF/PACF plots of weekly data of data over 5 years, but I just don't know where to go from ...
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Strucchange R package: correcting heteroskedasticity and autocorrelation [closed]

I’ve got a question concerning the R package strucchange that I use for testing and dating structural breaks in my PhD thesis. To be specific, I use the generalized fluctuation test framework with ...
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Good TS fit but no stationarity

I have yearly time-series that I want to predict, and for that I fitted an ARX (auto-regressive with a exogenous input) model to previous years (training set) and test it for the last year. My ...
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25 views

Do correlated error terms reduce predictive accuracy?

If error terms are correlated between observations, will that reduce how predictive a model is? Specifically, given the same predictor variables, will the mean square error of the model's predictions ...
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24 views

Linear models where the IV and DV both have temporal autocorrelation

I have weekly data from a lake over 3 months and I want to see if there is a correlation between concentrations of algae and richness of the bacterial community (number of bacterial taxa). However, ...
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39 views

An example of autocorrelation in residuals causing misinterpretation

I'm looking for an example of time series data where a regression of y~x has autocorrelation in the residuals that leads to misinterpreting the model. This is for a class demonstration where I would ...
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Regression in levels vs. regression in differenced form

I want to compute the following regression using R. lm(EurOis3~EurepOis3+Vstoxx+log(Open.Market.Operations)+CDS). I am using daily data(i.e. I have 5 observations ...
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Newey-West standard errors when Durbin-Watson test results are fine

I am running a time-series regression. The Durbin-Watson statistics is very close to 2. In such a situation, would it still be better to use Newey-West standard errors, or is it ok to use OLS standard ...
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Detrended Fluctuation Analysis: what does a exponent > 1 mean exactly?

Detrended Fluctuation Analysis is commonly used in order to identify long-range temporal dependencies in time series data. While white noise will have a DFA-Exponent of ~0.5, scale-free, long-range ...
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How can I test for changes in the distribution of categorical data over time?

Each week at my organization, we receive X number of type A messages, Y number of type B messages, Z number of type C messages...etc. I want to be able to test if the distribution of these message ...
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Algorithm calculating the autocorrelation time

I am in the middle of the analysis of a large set of Monte-Carlo data and you may know that calculating the autocorrelation of the Chain is a good part of the error estimation. I am doing this error ...
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Is a random walk + white noise modal an ARIMA(0,1,1)? [closed]

Let $Y_t=Y_{t-1}+\epsilon_t$ be a random walk and $Y_0=0$ Why is it true that the process $X_t=Y_t+\eta_t$, where $\eta_t$ is a white noise, so that $cov(\epsilon_t,\eta_s)=0$ for all $t,s$?
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How can I see sample autocorrelation from time series plot?

Lets say I am given time series plot. How can I estimate $r_1$ and $r_2$ which are sample correlation? I don't understand how to see correlation from data plot. I know how to get and use ACF and ...
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Why does adding a lag effect increase mean deviance in a Bayesian hierarchical model?

Background: I'm currently doing some work comparing various Bayesian hierarchical models. The data $y_{ij}$ are numeric measures of well-being for participant $i$ and time $j$. I have around 1000 ...
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When and why should one substracts mean before computing autocorrelation function

There are two definitions of autocorrelation function. The more popular among statistician is: $$ R(\tau) = \frac{E[(X_t - \mu)(X_{t+\tau} - \mu)]}{\sigma^2} $$ However the signal processing ...
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Test for autocorrelated variables

I would like to know if there is a good non-parametric test for detecting auto-correlation of one variable between all the observations of my dataset. I have 60 predictor variables for a statistical ...
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23 views

How would you find the variance of an autocorrelated error?

Given the equation $e_t = pe_{t-1} + v_t$, and given the values of p and $Var(v_t)$, how would you calculate $Var(e_t)$?
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Definition of Time Series

Time series model is defined as : A time series model specifies the joint distribution of the sequence ${\{X_t}\}$ of random variables. For example:$$P[X_1\le x_1,\ldots,X_t\le x_t]$$ for all $t$ and ...
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Blocks of variable size in k-fold cross-validation

I would like to make a custom k-fold cross-validation method for my data, by generating folds of auto-correlated observations. This would create many folds of variable size for test errors as well as ...
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ACF values in identifying non-stationarity

I have used NIST data to calculate ACF in excel which worked fine and coded in our programming language (NOT R). Here is the plot of ACF: Now my questions are: 1) From this ACF series how can I ...
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similarities between two signal using correlation

let say we have two signal ,there is given their time domain plots and also correlation plot and final correlation plot it should be noted that both signal have same spectral structure,they ...
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bootstrapping a regression with autocorrelated error

I have to verify that on two variables, $X_t$ and $Y_t$ hold the followings: $Y_t=\beta \times X_t+\varepsilon_t$ and that $var(Y_t)=\gamma \times X_t^2$. In order to give evidence / support to these ...
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regression with autocorrelated errors and specific error structure

I have to fit a linear regression model that takes into account both a specific - conditional variance relationship and a regression form $y_i=a+\beta \times x+\sqrt{\gamma \times x^2}\times ...
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Closed-form expression for autocovariance of random walk with drift

I am working through slides hosted at Basic Time Series Models, and am not sure how to mathematically derive a closed-form expression of the autocovariance of the "random walk with drift" model. The ...
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What is the best lag length for auto correlation?

I am doing a monthly rainfall forecasting model. I have monthly data from 1998 to 2012. I found in previous research that they have used partial autocorrelations and stepwise regression as an input ...
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89 views

Interpreting ACF and PACF Plot

My raw data consists of a 60-day time series with a downward trend. The data is weekly so the frequency is set to 7. I calculated the difference of the data which looks like this When I run ACF ...
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Incremental autocorrelation coefficient lag 1

I am a developer and I am trying to compute the autocorrelation coefficient of lag 1 incrementally. The problem is I have to test the results with some certified results from NiST Datasets. The ...
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Power spectrum of unlogged AR(1) process

Our variable of interest $X$ is nonnegative. We model $ \log(X) $ as AR(1) process. $ \log(X) $ power spectrum: $ S_{xx}(w) = \frac{\sigma^2}{1-\varphi^2} \frac{\gamma}{\omega^2 + \gamma^2} $ What ...
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Arima modeling with limited data

Our 250 weekly datapoints are shown in the figure, along with correlograms of 1st differences. Are we correct to conclude, from overdifferenced correlogram, that for this process we should have much ...
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Model for probability of N autocorrelated events

Say we have $N$ birds, $r$ is the probability that one bird sings. What is the probability $p$ that any of $N$ birds sings? If we assume independence, there is a simple model describing the ...
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Autocorrelation and Partial Correlation plots in ARMA models

Consider the following input and its Autocorrelation and Partial Autocorrelation plots (source). What are the shaded blue areas in these plots? I often see them when studying ARMA models. What do ...
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Spectral density estimation for limited data

We need an idea of the frequencies in the time series shown. What can we expect from nonparametric spectrum estimation? Observing that much power is in frequency 4 years, of which we have only one ...
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89 views

Robust OLS standard errors (Newey-West)

I am running a simple OLS regression with HAC adjustment (i.e. Heteroschedasticity and Autocorrelation adjustment) using the following function in hac() in matlab. ...
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Newey-West standard errors in OLS

I am trying to compute robust coefficient estimates for OLS, using the hac() function in MATLAB (see description of function in MathWorks). In my case, I am ...
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18 views

Statistical analysis of time to event data

If I have 2 events of interest, lets say $X$ and $Y$. I would like to know, what is the influence of $Y$ on $X$. It's like a correlation between 2 events, but I'm not sure what is the formal test for ...
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79 views

ARIMA Specification from Correlogram

How should I determine the data generating process from the correlogram below? This is non-seasonally adjusted monthly data that has been 1st differenced. I am trying to conduct univariate time ...
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Autocorrelation *across* random effects in nlme:lme?

I have response data measured at the site and month level. I wish to fit a year trend to the data and month to remove the seasonal trend. However, to avoid pseudoreplication, I have fitted year also ...
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Interpretation of the autocorrelation plot

This plot indicates the autocorrelation for a monthly time series of household gas consumption. This plot clearly shows a seasonality, I was wondering if the repetitive positive and negative ...
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89 views

How to test for serial correlation and ARCH effect in R package tsDyn?

I recently started playing around with the tsDyn package for R and successfully used it to estimate a bunch of VEC models and print their impulse responses (IRF) and error variance decompositions ...
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Auto-Correlation

I had thought that if I call acf() on a vector of integers, and examine the value correlation coefficient at K (lag) = 1, I would expect: A value close to +/-1 would show that the integers are not ...
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Can I remove seasonal autocorrelation through aggregation?

I have monthly time series data and there is autocorrelation? I can solve for this using lagged dependent variables and other methods and other models, then aggregate into annual terms. However, I ...
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Extracting information from auto correlation signal

I have an auto correlation signal that looks like this: This is an autocorrelation graph of a single column taken from a certain image using a CCD camera. You can see the autocorrelation strength ...
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25 views

Correlated cases and Cross Validation

I'm posting to ask if there is a method of cross-validation for correllated data that is already well implemented in R language. Some quick search on such method shows some techniques like h-block ...
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Inference from data with units of analysis in two distinct, but correlated, spatial hierarchies

I have a dataset on number of persons affected by a rare pollution-driven condition. The data is sparse and is stuctured at two spatial level: countries (n=35) and subnational entities (e.g. states; ...
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Interpretation of autocorrelation plots using ccf in R

I'm not that familiar with time-series type data. I am looking for some advice on the interpretation of the following plots of autocorrelation between two variables. I used ...
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61 views

Time-series and autocorrelation inequality

I am having problems proving for a weakly stationary process $\{X_t : t\in T\}$: $\rho_X(2)\geq 2 (\rho_X(1))^2-1$ where $\rho_X(j)=corr(X_t, X_{t+j})$. So far I have shown that $-1\leq ...