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 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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43 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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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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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
50 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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7 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
40 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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28 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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33 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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14 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
39 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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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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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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13 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
97 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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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
46 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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31 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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31 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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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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51 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
80 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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142 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 ...
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1answer
47 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
44 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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17 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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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 ...
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18 views

Test autocorrelation in irregularly(unevenly) spaced time series

I have a dataset that includes observations at different time points. There are multiple observations at the same time points and the time points are not evenly spaced. Now, I would like to test ...
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2answers
89 views

A question about an autocorrelation plot

I obtained an ACF plot from R. Please see below: Does that mean the observations are independent? What do small autocorrelations imply?
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39 views

autocorrelation in evaluating time series forecasts

I'm having some trouble wrapping my head around whether using Holt-Winters ETS or an ARIMA model for forecasting sales figures (which are highly seasonal). I'm been using R and the Forecast package ...
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21 views

Should I do this ARMA model?

These are the autocorrelations: As one can see, it is quite low around 0.02 for the first lag. But it is significantly nonzero, as the blue lines indicate. However, I dont think it makes sense to ...
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68 views

Conceptual Question: Autocorrelation of autoregressive process

An AR(1) process: $X_t = c+\theta X_{t-1} + \epsilon_t$ where $\epsilon_t$ is a zero mean white Gaussian noise. The Autocorrelation matrix is expressed by the formula mentioned in the Wikipedia ...
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52 views

Auto correlation function of AR(p) process

I am doing a time series course and in the theory part there are few things I don't understand.In obtaining auto correlation function for AR(p) process it is done as: AR(p)=$X_t = α_1X_{t−1} + ...
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33 views

Diagnose ARIMA seasonality model residual auto and partial correlation plots

I have two and half years of the weekly time series data. The seasonally period is 52 weeks. I differed the data with log transformation and feed the data into the MATLAB arima model. ...
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Should I check the z-score if the p-value of Local Moran's I is significant?

The dataset I'm using contains income data per area. The values are not normally distributed as shown in the following diagram. Global Moran's I indicates significant spatial patterns and Local ...
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65 views

3 month forecast for commodity prices in R - general help for approach

In the following I'll describe my undertaking as detailed as possible in order to provide you enough information. Please keep in mind (when answering) that neither I'm a matematician nor a ...
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1answer
74 views

Time Series Function - Constant vs Piecewise

I have daily data for online marketing $ spend and the number of clicks to the website gained. I want to determine a function that 'maps' the two together. I cannot use normal linear regression ...
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67 views

Time series with correlated observations: How to start analysis?

We have a time series dataset: Daily arrivals of asylum seekers. Goal is to model this variable. In particular we would like to attempt Arima modeling and/or fitting a distribution. Before we get to ...
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10 views

How can Durbin-Watson and SPEC give Opposite Results?

I am modelling house prices against sales amount using a simple linear regression model. My SPEC (Option in SAS) says IID (p-value > 0.05) but my DW (Option in SAS) says a strong 1st order ...
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17 views

On the derivation of the closed form Yule-Walker moment estimator of a GARCH(1,1). (exercise)

The exercise states: (Yule-Walker estimator) GARCH models are typically estimated by a numerical implementation of maximum likelihood methods. This procedure has the disadvantage that it does ...
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72 views

On the Autocorrelation Matrix of an ARMA(2,2) to derive the Yule Walker Equations

For an AR(2) I can get the Yule-Walker equations: $$\begin{cases} \rho_1=\alpha_1+\alpha_2\rho_1 \\ \rho_2=\alpha_1\rho_1+\alpha_2 \\ \rho_k=\alpha_1\rho_{k-1}+\alpha_2\rho_{k-2} \end{cases}$$ ...
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34 views

How to improve linear model generalization when autocorrelation is present?

I have features $X_t$ and response $Y_t$ (all continuous variables) and my objective is to find the best estimate of $f(X_t)=Y_t$ where $f$ is linear, and 'best' is defined as lowest generalisation ...
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164 views

How to interpret autocorrelation plot in MCMC

I am getting familiar with Bayesian statistics by reading the book Doing Bayesian Data Analysis, by John K. Kruschke also known as the "puppy book". In chapter 9, hierarchical models are introduced ...
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134 views

stationarity in time series

I'm learning a Time series course and I have a few questions. Strictly stationary is a process if the joint distribution of $X_{t1},X_{t2},...,X_{tm}$is the same as the joint distribution of ...
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37 views

Autocorrelated predictor bias correction in R

I am looking for a procedure to correct for bias caused by autocorrelated predictors in a simple linear regression. The predictor is a sentiment indicator ot a weekly survey where a certain percentage ...
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29 views

Test for serial correlation

I have an OLS model with macro-economic variables like GDP, Unemployment rate as my independent variables. While testing for serial correlation up to order 4 with Breusch–Godfrey test (using proc ...
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1answer
578 views

How to interpret ACF and PACF plots

I just want to check that I am interpreting the ACF and PACF plots correctly: The data corresponds to the errors generated between the actual data points and the estimates generated using an ...
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45 views

How to calculate the lag 1 autocovariance for the difference of two variables from the individual autocovariances of the two variables

Is it possible to calculate the auto-covariance of the difference of two variables, from the auto-covariances of two variables being differenced? I have a situation where: Y=βx x is 3*3 matrix of ...
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52 views

My transfer function has non-stationary inputs, but a stationary output. Should I difference both the inputs and outputs during structure estimation?

I have a system of two inputs and one output that I'd like to model using the following Box-Jenkins transfer function ("dynamic regression") structure: $$y_t=\frac ...