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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What does the following ACF curve mean ? (Picture attached)

I was checking for seasonality and other dependencies and this is the curve I get . There's no apparent seasonality....but what exctly does the falling slope mean? Any help would be appreciated. ...
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18 views

Vector Autoregressive Model: residual's kurtosis proportional to number of lags?

I have some transformed data set (windspeeds that are nearly-weibull-distributed). I transformed this data which results in near-normal distribution (close to no excess kurtosis and skewness of zero). ...
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12 views

Which time series model to use?

Hi I have a large data set of objects, each containing a list of the same attributes. The data is arranged in a time series so that the value for an attribute for an object is indexed by its time. ...
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11 views

correct for temporal autocorrelation in mantel tests

Hej, I want to compare the community composition of a bacterial assemblage with it's resource use ability. therefore I calculate a distance matrix based on the community composition and a distance ...
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1answer
30 views

Do we need to detrend when do Cross-Correlation between two time series?

I have a group of time series variables and I want to found out the relationship among them. The method I use is to calculate pair-wise correlation between two time series and found out those with ...
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35 views

Dealing with nonstationarity and autocorrelation

Relationship between interest rates and retail sales. I have a time series sample of quarterly data for 10 years. My dependent variable is retail prices and independent variables are interest rates, ...
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24 views

Sampling Distribution of Sample Correlation Coefficient

For a linear process $X_t=\mu+\sum_j\varphi_jW_{t-j}$ where $W_t$ is white noise and $\mathbb E(W_t^4)<\infty$ , $$ \begin{pmatrix} \hat\rho(1) \\ \hat\rho(2) \\ \vdots \\ ...
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Exactly The Same Autocovariance Function of Two Time Series

A MA(2) process : $$X_t=W_t+\frac{5}{2}W_{t-1}-\frac{3}{2}W_{t-2}$$ where $\{W_t\}\sim WN(0,1)$ And another MA(2) process : $$X_t=W_t-\frac{1}{6}W_{t-1}-\frac{1}{6}W_{t-2}$$ where $\{W_t\}\sim ...
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Mixed effects model with autocorrelation between fixed and random effects

I have never posted here before, so apologies if I do not follow the correct format. My experiment design is I have 12 reps each of 4 different species of plant which I experimented on in 2 blocks, ...
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35 views

Modeling proportions of autocorrelated binary data

I have data on infant crying for three time periods -- 1994-1996, 2000-2002, and 2010-2013 -- with about 15 infants per year. Each infant was observed every minute for 1080 minutes (across 3 days). If ...
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19 views

Autocorrelation in R

I have a data structure as below. There are few experiments where height was measured in different ages (max 5 observation per experiment, min 2). ...
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18 views

Compare distributions in time series

I have a time series (weekly sales data), on which i have made an intervention analysis (to be specific a VARIMAX). The intervention (increased opening hours) ended out being insignificant. But what i ...
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14 views

Autocorrelation for Time-series Crossection data

I am examining whether the market reaction (Y) is influenced by a number of X's variables. My data is gathered per firm at time t. If I understood correctly, this is called Time-series Cross-section ...
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10 views

On the correlation function of a stationary time series (spectral analysis)

I am following a proof of the following fact of which I do not understand only the last step. I will post it entirely for the sake of completeness but do not hesitate to just look at my question at ...
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11 views

GAMM - error when using spline smoother, only allowed to use tensor product

I am familiar with the basics of statistical regression models, including GAMs, but I am stumped on a particular implementation issue. I am constructing a GAMM to fit to data that is autocorrelated. ...
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8 views

How to determine the optimal time averaging window

I have two large time series datasets with some background noises. I would assume the two datasets are either lag correlated or lead correlated. I tried to use time averaging to smooth out the dataset ...
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11 views

How to find covariance matrix from correlation if mean is not given?

I'm given autocorrelation function of gaussian random process: $$ R_x(\tau) = 3e^{|-\tau/3|} $$ Now I should find covariance matrix. I know the formula and solutions, where $$ C_{xx} = R - E[X]^2 $$ ...
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Autocorrelation in DOLS: will HAC standard errors work?

I am currently estimating a cointegrating regression (DOLS), where my residuals have autocorrelation. Sometimes it is just in one or two lags, but sometimes it is more. My question is: Can I apply HAC ...
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37 views

Breusch-Godfrey Test for autocorrelation

Following the steps of Breusch–Godfrey test , I wrote my own R code which differs from the R function for ...
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11 views

Wald–Wolfowitz runs test

How does the formula of mean and variance of Run test come ? That is , How to derive those formula ?
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32 views

Does possible autocorrelation in data affect simple correlations?

I have a question concerning autocorrelation in data affecting correlation coefficients. Consider a time series of stock returns (e.g. 10 trading days) of different stock markets (A, B, C and D) and I ...
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22 views

What is a Summary Autocorrelation Function (SACF)?

Seen this in a few papers regarding ACF-based pitch detectors, e.g. in http://staffwww.dcs.shef.ac.uk/people/G.Brown/pdf/casareview05.pdf p. 7-8 where they give you the equation for $S(t,τ)$. but ...
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Mean of Empirical Auto-Covariance

Chris Chatfield's "The Analysis of Time Series: An Introduction" 6th ed, gives the mean of the empirical auto-covariance as: E(r_k)=-1/N where E is the expectation r_k is the empirical ...
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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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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 ...
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60 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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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 ...
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1answer
60 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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38 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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22 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 ...
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1answer
51 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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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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19 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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92 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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88 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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18 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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25 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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39 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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31 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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22 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
27 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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69 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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223 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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31 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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17 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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456 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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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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39 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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33 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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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 ...