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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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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16 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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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
49 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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112 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
34 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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42 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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27 views

Pre processing methods to reduce autocorrelation in Time Series [on hold]

I have an eeg time series data set. Can you suggest some pre processing methods to minimize auto-correlation in time series data? Can PCA and Fourier transformations be taken as methods to reduce auto ...
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16 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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4answers
87 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 ...
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9 views

Obtain the graph of the autocorrelation function in ARIMA models [migrated]

I am implementing an ARIMA model in Python for forecasting U.S. GDP. I am interested in obtaining the graph for the autocorrelation function. I obtained the values for ACF but I can not see the ...
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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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86 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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32 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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52 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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42 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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24 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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54 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
69 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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1answer
55 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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8 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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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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56 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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33 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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117 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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113 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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30 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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24 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
334 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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34 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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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 ...
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How you calculate the Autocovariance for this function?

$X(t)$ is RV with mean zero and auto covariance $cov(x)= \exp(-|t|)$ find the auto covariance of this function $y(t)= \int x(u) du$, from 0 to $t$ where $t > 0$
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270 views

Forecasting a seasonal time series in R

Forecasting airline passengers seasonal time series using auto arima Hi, I am trying to model some airline data in an attempt to provide an accurate monthly forecast for June-December this year using ...
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42 views

Univariate fixed effect Vs Multivariate model -Negative Covariance, positive parameter estimate, but why?

I am trying to compare the results of two models. The first model looks at y with x as a fixed effect. The second looks at the covariance between x and y. Both models have repeated measures for x ...
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Quantity like correlation

I want to calculate this sort of quantity, $f()$, for my data. $x$ and $y$ are time series. $f$ behaves like a pseudo-correlation, but is different in the sense that even if the values jump up and ...
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165 views

Why autocorrelation affects OLS coefficient standard errors?

It seems that OLS residuals autocorrelation is not always an issue, depending on the problem at hand. But why residuals autocorrelation would affect the coefficient standard errors? From the Wikipedia ...
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39 views

when should I need to be concerned about autocorrelation?

I have a series of wave heights observations (2observations per hour for each day in 7 months) and I'm trying to model a regression with wind data (same frequency of observation). Since waves ...
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55 views

Why does Random Forest Regression perform worse than autoregression

I have a dataset of NFL games. Each game has one row for each team in the game. Each team's row contains the team's statistics in that game (such as points scored, passing yards, red zone attempts, ...
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89 views

Matlab: Unable to plot partial autocorrelation plot

For a time series I wanted to plot separately the partial auto correlation. Below is the graph for a time series which shows PACF plot of the time series $x$ which I wanted to reproduce: This ...
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39 views

How is the impulse-response function of a given system related to the autocorrelation function?

If I have the autocorrelation function of an observed system output, how does this relate to the impulse-response function of that system, if I don't have information about the input?
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53 views

Rule of Thumb for minimum length of time series for Autocorrection estimation

I had a related question answered here: Rule of Thumb for minimum length of time series for AR(1) estimation However the answer gives rise to a new question. I want to be able to estimate the Auto ...
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Rule of Thumb for minimum length of time series for AR(1) estimation

I have a data set of 350 points, I want to estimate the lag 1 auto correlation for different sub-sets of the data. More precisely I want to take non overlapping windows of length 1,2,3....n and ...
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109 views

Detecting whether website visits are automated

I am trying to detect automated visits to a website. A typical data set for an automated client is of the form: ...
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2answers
171 views

Is residuals autocorrelation always a problem?

I read that OLS underestimates variance when residuals are autocorrelated. I see why autocorrelation would be a problem in time series analysis, in the sense that the coefficient are not efficient ...
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Interpretation of the partial autocorrelation function for a pure MA process

I have been working with some time-series theory and I noticed something that I can understand "mathematically", but not based on the intuitive explanations of what the partial auto-correlation ...
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37 views

Variance-covariance matrix as the sum of variance covariance matrices

I have a variance-covariance matrix, $\mathrm{V}$. This allows me to take a vector, $x$ of independent random variables drawn from a known distribution, and induce a required variance-covariance ...
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108 views

Binning method: looking for an example

I heard and read several times of the use of 'binning' methods to estimate the uncertainty and the auto-correlation time of a sample generated by MCMC but I can't find a textbook example of it being ...
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196 views

Library routine for rolling window lag 1 autocorrelation?

I am looking for a library routine that will calculate the lag 1 autocorrelation of a time series with a rolling window; meaning "slide a window of size N points along the time series, calculate the ...