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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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)? [on hold]

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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1answer
22 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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2answers
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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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1answer
28 views

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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1answer
28 views

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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1answer
37 views

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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2answers
52 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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clustering discrete data - how to get “autocorrelative distance” matrix?

I'm trying to cluster discrete (histogram) data with unequal bins. I came across the post: Clustering distributions and calculated the cumulative sums of each data set and interpolated between ...
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23 views

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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17 views

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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1answer
16 views

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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2answers
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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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45 views

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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1answer
47 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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2answers
81 views

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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1answer
67 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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1answer
30 views

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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1answer
52 views

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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1answer
66 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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27 views

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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1answer
11 views

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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24 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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1answer
60 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 ...
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Is autocorrelation also a problem with data collected from different respondents?

I have a question regarding autocorrelation in multiple linear regression. I analyse data on IPOs over 6 years. I look at a dataset of 450 companies which have listed their stock at the stock ...
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1answer
67 views

Interpreting Auto correlation of Human walk data

My auto correlation coefficients plot of human walk looks like this. This walk data is recorded with accelerometer sensor inside the pocket. Human walk is periodic, and I need to determine that period ...
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29 views

Autocorrelation function in R for observational data

I'm trying to replicate an analysis done in Stata with R that involves calculating the autocorrelation for a particular outcome measured in many different areas. I've already run a linear regression ...
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1answer
100 views

Distinguish an ARMA and an ARIMA model graphically

I'm currently analyzing some time series data and I need to know how to distinguish an ARMA model from an ARIMA model just by looking at the auto-correlation function and partial auto-correlation ...
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34 views

Missing data in Multilevel Longitudinal Model with Stata

I normally use xtmixed in Stata to test hierarchical linear models (e.g. performance of students nested in schools). Now it's the first time I need to test a ...
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1answer
147 views

Feasibility of Negative Binomial Spatial Regression

I have a set of crime count data where it appears that the data take on a negative binomial distribution. I have had some success converting the dependent variable (a crime count) into a rate and then ...
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10 views

Can you specify AR(p) structure for cyclic spline in mboost?

Suppose I fit want to fit a boosted GAM using mboost:gamboost to time series data. Is it possible to specify an AR(p) structure for the cyclic component following a ...
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1answer
50 views

What is “Targeted Maximum Likelihood Expectation”?

I'm trying to understand some papers by Mark van der Laan. He's a theoretical statistician at Berkeley working on problems overlap significantly with machine learning. One problem for me (besides ...
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34 views

Mixed-effects models: autocorrelation for data with gaps in R

I wonder if there is a way of modelling of an autocorrelation for data with gaps in mixed-effects models in R? In addition, I would like to model heteroschedasticity. Thanks!
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statictical method to check for autocorrelation? [duplicate]

A model was developed to estimate monthly reserve money growth. To further check if the estimated model adequately represents the time series, a check for autocorrelation has to be made. Which ...
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302 views

How to apply heteroskedasticity and autocorrelation tests to panel data in eviews 8?

I am trying to test for heteroskedasticity and/or autocorrelation in my fixed effects panel regression in Eviews 8. There do not appear to be the necessary tests available. The Breusch-Pagan LM test ...
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MANOVA on autocorrelated variables

I am trying to find out if signals 1 and 2, can explain signals 3 to 10. All signals are continuous and time-varying and are rather strongly autocorrelated. Signals 3 to 10 (my dependent variables) ...
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What is the auto-covarriance of a stationary AR1 process?

Say a stationary AR(1) process is given by: $$ X_t = c + \phi X_{t-1} + \epsilon_t $$ where $ \epsilon_t $ is a white noise process with zero mean and constant variance $ \sigma^2 $. Wikipedia ...