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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Why ever use Durbin-Watson instead of testing autocorrelation?

The Durbin-Watson test tests the autocorrelation of residuals at lag 1. But so does testing the autocorrelation at lag 1 directly. Plus, you can test the autocorrelation at lag 2,3,4 and there are ...
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30 views

Where is the dominated convergence theorem being used?

I am trying to fully understand the proof of a theorem, I only have a problem with the application of the dominated convergence theorem. For the sake of completeness I will upload the whole statement ...
2
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1answer
53 views

Property of the autocovariance function in time series

In the framework of time series analysis Why does $\lim_{n \rightarrow \infty} n^{-1} \sum_{|h| <n} |\gamma(h)| = \lim_{n \rightarrow \infty} 2|\gamma(n)| $? The LHS (left hand side) sequence of ...
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23 views

Error on histogram computed on autocorrelated time series

I am struggling to find an answer to this quite basic question. When computing a histogram on a time series which has some correlations (i.e. measurements are not independant), how to estimate the ...
2
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1answer
50 views

Understanding the Durbin Watson test

The test statistic for the Durbin Watson test can range from 0-4 from what I have gathered. Now the lower limit of 0 makes sense considering the test statistic consists of two summations which are ...
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33 views

Estimating AR process for Logistic Regression

I'm fitting a time-series model with independent $X$ variables coded as months of the year (so there are 12 of them) and the dependent $y$ variable is some proportion, bounded between 0 and 1. As a ...
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21 views

What non random patterns in a series Autocorrelation cannot detect

I know there are complex patterns in a series that cannot be detected by autocorrelation... but I cannot find what types of patterns these are. Can anyone provide an instance where the autocorrelation ...
0
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1answer
40 views

What does it mean to normalize the data by the autocorrelation at the 0-th lag?

I'm just digging into python as a newbie and saw this expression in the plot docs: normalize the data by the autocorrelation at the 0-th lag. I didn't see further details, and Google wasn't very ...
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13 views

How to Compute the Integral of the Auto-correlation Function for a Discrete Time Series

Using the covariance $$ c(u) = \frac{1}{N}\sum^{N-u}_{t=1}(x_t - \bar{x})(x_{t+u}-\bar{x}), $$ I've computed the auto-correlation function $$ r(u) = \frac{c(u)}{c(0)}, $$ where $x$ is a time ...
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18 views

variance of autocorrelated series

I have simulated a series with autocorrelation of 50%. When I compute the variance of the series it is 1/2 of the variance of the white noise series. Could somebody show me the math behind this ...
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2answers
69 views

Can you solve (avoid) an autocorrelation problem by adding an independent variable?

I am working on modeling what amounts to a time series, the DV is measured 40 times a day on 40 different days--- the actual timing of measurements on a given day varies, and the number of days ...
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2answers
75 views

Is there a remedy for removing autocorrelations from residuals of seasonally fitted ARIMA model?

I fitted a number of SARIMA models using R and chose the ARIMA(0,0,0)(3,1,0)[12] as the best fitted model to the univariate data with 180 points (periodicity=12). This model is chosen as the best ...
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13 views

Autocorrelation in random effects model

I am doing a random effects regression that has first order autocorrelation. When I use a robust method, my results turn insignificant. But if I exclude time dummies from the robust regression, my ...
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20 views

Analysing the correlation between two trends

I've got 2 growing trends. One is the input (the number of published articles on a website) and I want to understand if the other appears to be correlated (the number of daily visitors). The problem ...
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1answer
31 views

How to calculate $\phi$ (phi) - a first order autocorrelation coefficient

I have a dataset of historical quarterly earnings per share for 8 years. I am trying to use the following formula for the purpose of estimating earnings: $E(Q_t) =Q_{t-4} + \phi_1(Q_{t-1} - Q_{t-5}) ...
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16 views

Concerns regarding correlation structures and random variance using lme

I’m modeling some variables repeatedly measured over a three months period for a total of 300 individuals. These variables (e.g. activity) were measured at three different time scales: daily (90 ...
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1answer
15 views

Autocorrelation and Statistically Independent Samples

I'm trying to do an error analysis and I was asked to calculate the confidence intervals but was told that I need to calculate the true number of statistically independent samples for doing this. I am ...
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1answer
23 views

Testing data for regular oscillations

This is a little hard to explain, but I would like to test data for periodic oscillations, but not necessarily oscillations of the same amplitude. for example (crudely!): So basically I want to ...
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38 views

Choosing the parameters for an artificial neural network for time-series regression in R

I'm trying to build an artificial neural network (ANN) using the R "neuralnet" package, to predict streamflow from snow albedo (reflectance of the snow; controls the amount of heat absorbed by the ...
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3answers
132 views

How to interpret this autocorrelogram graph?

I am new to statistics. I found a script which makes a autocorrelogram graph(see attached) of spike timings of a neuron. I got the graph but I am not able to interpret it. Matlab Code below. ...
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1answer
27 views

Computing Issues with Kriging

I am having some issues with Kriging in R, and I was looking for some idea where I am going wrong. From what I can tell, I done a decent job removing the trend, and I believe my transformed data is ...
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12 views

How to fit an logistical autoregression in R?

I modeled the relationship of $X$ and $Y$ by the logistic function. The residual plot displays autocorrelation which I'd like to rid. I want to try adding trend component to $X$, thus the model ...
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325 views

Testing for autocorrelation: Ljung-Box versus Breusch-Godfrey

I am used to seeing Ljung-Box test used quite frequently for testing autocorrelation in raw data or in model residuals. I had nearly forgotten that there is another test for autocorrelation, namely, ...
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21 views

What are good values for autocorrelation, Gelman, and cross-correlation in rjags?

I don't want to post my whole code since it is long, so I will only post part of it: ...
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0answers
29 views

panel data with serially correlated independent and dependent variables

I have a panel data where the independent variables are serially correlated (macro-economic time series), also the dependent variables (company sales growth) are probably serially correlated. Here ...
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25 views

How can I compute multicollinearity (VIF) in R, and know if it's safe?

I am working on a group project for a university course on "big data research methods". My data is aggregated by neighborhoods in Chicago. My dependent variable $Y$ is the property crime rate (per ...
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28 views

Heteroskedasticity and autocorrelation in simple linear regression?

While looking through a simple linear regression, I noted the presence of both heteroskedasticity and autocorrelation, and am looking to understand the consequences of each. On this project, I am not ...
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1answer
44 views

Autocorrelation definition

I am formatting a statistics proof, and I wanted to make sure that I have the definition of autocorrelation correct. Is it the case that the autocorrelation of a continuous variable is the same as ...
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0answers
11 views

General advice on modeling clustered data

I have biomass data from ~100 sites which I wish to relate to site environmental characteristics, and then based on those relationships predict biomass (gm2) across synopic layers of surrogate data in ...
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1answer
36 views

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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41 views

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 ...
3
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1answer
80 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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0answers
42 views

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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63 views

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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23 views

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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1answer
30 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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1answer
25 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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1answer
50 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 ...
0
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1answer
65 views

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 ...
3
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1answer
60 views

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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14 views

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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27 views

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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0answers
24 views

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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0answers
47 views

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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1answer
59 views

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 ...
11
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1answer
133 views

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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19 views

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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18 views

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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1answer
25 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 $Var(e_t)$?