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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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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12 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
76 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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25 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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46 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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1answer
33 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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1answer
18 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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47 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
68 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
53 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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7 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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11 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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1answer
53 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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26 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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1answer
84 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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1answer
106 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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23 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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22 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
161 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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23 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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1answer
33 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 ...
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15 views

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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1answer
195 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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28 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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33 views

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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1answer
142 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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36 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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48 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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84 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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1answer
27 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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47 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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48 views

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
156 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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51 views

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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34 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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1answer
105 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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3answers
160 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 ...
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1answer
77 views

Residual autocorrelation versus lagged dependent variable

When modeling time series one has the possibility to (1) model the correlational structure of the error terms as e.g. an AR(1) process (2) include the lagged dependent variable as an explanatory ...
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2answers
108 views

Why is it desirable to have low auto-correlation in MCMC?

I keep reading about the need to check for autocorrelation in MCMC. Why is it important that the autocorrelation is low? What does it measure in the context of MCMC?
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1answer
46 views

Is the Durbin-Watson test appropriate for count data

In determining if there is any serial correlation in a time series of count data, is the Durbin-Watson statistic or similar approaches appropriate? I ask this question because the dwtest implemented ...
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1answer
150 views

Getting Residuals to be White Noise

I'm on a time series project for an undergraduate course. For the project I'm trying to come up with an ARIMA model for the housing starts data set. ...
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90 views

Estimation of regression with autocorrelated errors

In a book it is written that, In regression work we typically assume that the observational errors are pairwise uncorrelated. But in most time series data , the successive residuals have tendency to ...
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17 views

Two-tailed test [duplicate]

In one-tailed test , we give our decision at $\alpha$ level of significant. But in two-tailed test , why do we give our decision at $2\alpha$ level of significant? Why do we not give the decision of ...
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1answer
54 views

Spatially auto-regressive two-stage model

I'm working on a project in which I use a 'Generalized Spatial Two-Stage Least Squares' model, mostly known as $y= X \beta + \lambda W y + u$ and $u = \rho M u + \epsilon_n$ where $y$ and $u$ are ...
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119 views

Durbin Watson test statistic

I applied the DW test to my regression model in R and I got a DW test statistic of 1.78 and a p-value of 2.2e-16 = 0. Does this mean there is no autocorrelation between the residuals because the ...
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44 views

Extremal serial dependence

As part of my analysis of heavy-tailed time series of company returns, I would like to check whether extreme returns exhibit serial dependence, i.e. if extreme events are followed by extreme events. ...
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113 views

ACF and PACF plot analysis

I am new to ARIMA, and I am trying to understand these lag plots. Are the following ACF and PACF suggesting that the lag of my time series is 4? If I am wrong, please help me understand these plots. ...