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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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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23 views

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
14 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
58 views

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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1answer
35 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
21 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
57 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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62 views

Is autocorrelation a serious issue [closed]

Will you consider auto-correlation as a serious issue in this case? One of the models I test is written in R ...
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14 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
55 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
19 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
51 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
40 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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24 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
9 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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9 views

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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1answer
22 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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8 views

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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25 views

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
58 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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1answer
27 views

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
61 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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26 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
92 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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26 views

Model selection and performance evaluation using cross-validation for time series with missing values

So my task is to select and evaluate a statistical model (random forest, boosted trees, neural networks etc.) for a time series with missing values around 10 years long. One of the goals of that is to ...
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28 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
108 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
46 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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31 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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12 views

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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147 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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18 views

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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1answer
42 views

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 ...
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55 views

Bootstrapping with standard deviation, mean and autocorrelation

I found in the matlab examples a way to use mean and sd for bootstrapping: ...
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32 views

Calculate prediction interval for SAR model (errorsarlm function in R)

I would like to predict prediction interval for a SAR model (function errorsarlm in R - package spdep). While the function predict.lm allows to set interval='prediction' parameter to predict the upper ...
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23 views

How can I evaluate spatial autocorrelation in a binomial GLMM?

Following Dormann et al 2007 Ecography, I have employed a GLMM approach in R to account for spatial autocorrelation in a binomial regression model (logistic regression) that does not have random ...
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1answer
158 views

Should we test error terms for auto correlation or multicollinearity

I understand the basic difference in definition between multicollinearity and autocorrelation. I.e multicollinearity describes a linear relationship between whereas autocorrelation describes ...
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26 views

GLM and temporal correlation [closed]

I work with marine mammals stranding time series from 1976 to 2013. The idea was to model the number of marine mammals stranding on the beach (response variable) using year and month as an explanatory ...
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1answer
57 views

Does ADF test regression remove all autcorrelation? (Do we really know with 100% certainty that ADF-resulted-regression has no autocorrelation?)

The goal of ADF is to test whether we have unit root or not. DF (Dickey-Fuller) test equation (regression equation) may include autocorrelation, and its result is not so reliable. In ADF, ...
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40 views

Correlation and coefficient with overlapping data

I have a time series data, with 5-period rates sampled at 1 period intervals. Essentially $$r_i = x_{i+5} - x_i ; ~~ i=1,...,N-5$$ This creates an overlapping data problem for regression. As far ...
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1answer
39 views

Simulating a data generating process

Suppose I wanted to simulate the data generating process of a non-linear regression with ma(1) errors. So, without going into many unnecessary details, the model is $$y_t = f(x_t,x_t-1,..., x_{t_0}, ...
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30 views

Auto-correlation vs. number of observation periods

I've just read an excellent post mix model I've a question connected to that. Roland, can you recommend any reference to a comment that if one have not enough observation periods then it is ...
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98 views

Panel data with N < T heteroscedasticity and autocorrelation. Should I include country dummies?

I have panel data of $N=18$ countries with $T=72$ months. Heteroskedasticity and autocorrelation are present in the dataset. I was working in Stata with xtreg fixed ...
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1answer
102 views

ACF and PACF Formula

I want to create a code for plotting ACF and PACF from time-series data. Just like this generated plot from minitab (below). I have tried to search the formula, but I still don't understand it ...
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1answer
168 views

What does my ACF graph tell me about my data?

I have two datasets: My first dataset is the value of an investment (in billions of dollars) against time, each unit time being one quarter since Q1 of 1947. The time extends to Q3 of 2002. My ...
2
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1answer
75 views

Correcting for spatial autocorrelation in dissimilarity datasets

I have a community assembly dataset with 299 species at 15 sites. Im interested in correcting for the effect of spatial autocorrelation on beta-diversity (or species turnover). Dataset here. There is ...
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1answer
46 views

Problems with seasonality removal

My problem is similar to this one from stack overflow: http://stackoverflow.com/questions/23568275/cannot-remove-time-series-seasonality I'll provide some data and make it more detailed. Please keep ...
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18 views

Testing for Changes in Autocorrelation Levels following Shock

I'm working with an (unbalanced) panel data set. I'm interested in testing whether the autocorrelation of a variable, $F_{it}$, changes following a sudden event $Z_t=1$, where $Z_t \in \{0,1\}$, ...
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112 views

Time Series for each customer

Is it possible to create Time Series Analysis for each customer? Say if have 100 customers and I wanted to predict how much amount they are going to spend next. I have done the Time Series for the ...