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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AR(1) on autocorrelated data that is not a time-series

I need to apply a regression model on observations that is not time series data but each observation presents a store and the amount of cartons that gets sent to that store. For instance ...
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34 views

Combining two autocorrelation functions measured on same stationary process

I have two autocorrelation functions measured from the same stationary process, but the two measurements were taken with different instruments that measure different lag times. I would like to ...
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11 views

How would you test for high order autocorrolation

The question is the following; And I determine the intervals If I Will do breusch-godfred test, I guess accourding to these interval, I can find high order correlation. But I dont know how to ...
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140 views

Differencing a time series

I am looking to find the ACF of a time series, but after it is differenced. $y_t = a_1y_{t-1} + \epsilon_t , \mid a_1 \mid < 1$ I understand that to find the ACF this process needs to be ...
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35 views

Forecasting and auto-correlation [duplicate]

I'm reading this chapter forecasting principles and practise from a forecasting book. The author has explained a linear regression model. Now this linear regression model will definitely have some ...
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16 views

Johanson test conditions and Breusch-Godfrey LM test

I am a student from Belgium and I am making a thesis about the relationship between credit aggregates and property prices. I examine the Granger causality between the two variables and I also do some ...
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2answers
54 views

Intuition behind auto/cross-correlation

I am really having trouble understanding the intuition behind autocorrelation. I mean why are we even calculating a correlation of some series with itself? Can anybody explain it in lay terms with an ...
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27 views

How to interpret the characteristic roots of moment equation of a AR(2) model?

I am learning the financial time series using the book 'Analysis of financial time series' by Ruey Tsay. In chapter 2, they introduced AR(2) models. The moment equation (which is the function between ...
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35 views

Variance of the sum of correlated random variables

i'm trying to compute the variance of the random variable $$X = \frac{1}{N}\sum_{i=1}^N x_i$$ where $x_i$ are correlated identical random variables (mean and variance defined) obtained from a ...
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123 views

What is the autocorrelation function of a time series arising from computing a moving standard deviation?

Say I have a time series of observations and I compute a measure of the variance of that time series as the standard deviation (SD) in a rolling window of width $w$ and that window is moved in single ...
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7 views

How can I compare the deviation from CSR in different point patterns?

I recently discovered the many tools of point patterns analysis and this is a very interesting field. I read a lot about how to look for deviations from complete spatial randomness (CSR) and I am ...
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23 views

Spatial auto-correlation test for binary data in R [migrated]

I want to test a species' presence / absence records for spatial autocorrelation. My data contain >130,000 grids in GIS and with about 700 species' presence records. I have read that the normal ...
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56 views

Interpreting Durbin-Watson results

I have fitted a glm to my data set and used to the Durbin-Watson test to check model fit. I have obtained the result. How can i interprete it? ...
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14 views

How to determine the proper sets or subsets of outcomes when autocorrelating frequency of each from year to year

I am trying to determine whether a baseball player has the ability to influence the outcome of an "at bat" by calculating the correlation coefficient between the percentage of at bats which result in ...
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1answer
58 views

How to account for autocorrelation in a multiple linear regression?

I'm trying to create a multiple linear regression with water temperature change as my response variable and four numeric explanatory variables (that influence temperature change). Each numeric ...
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1answer
17 views

Variance of an autocorrelated random variable two periods in the future with Bayesian updating

I observe draws of some random variable $Y$ over time where $Y_{t} = aY_{t-1} + \epsilon_{t}$. $\epsilon \sim N(0, 1/\rho_\epsilon)$ and $a$ is an unknown parameter with prior distribution $a \sim ...
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35 views

When is the autocorrelation function of a stationary process decreasing/nonincreasing? Markovian?

When is the autocorrelation function of a stationary process strictly decreasing or nonincreasing? Can being Markovian make it true? When is the autocorrelation function of a stationary process ...
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15 views

Non-parametric 2-sample test for correlated data

I have two samples of data, S1 and S2, that both suffer from spatial autocorrelation. The samples are different sizes and are not paired (specifically, S1 is comprised of M subsamples of k spatially ...
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19 views

Should one remove all autocorrelation?

Or is an AC of say less than 5% (in the residuals) acceptable for continuing with usual Panel Data analysis?
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139 views

How to interpret ACF and PACF and compare with Ljung Box result

I took the residual of a historical stock price $\hat e_t=r_t-\hat \mu_t$, where $r_t$ is the return of a stock and ran ACF and PACF. From the ACF I think that the residual does not follow AR or MA ...
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95 views

Sample ACF and PACF of a random walk

Suppose $X_n$are iid $N(0,1)$ random variables. Define $S_n := \sum_{i=1}^n X_n$. Then $S_n$ is a random walk. Since $Var(S_n) = n$ and $Cov(S_n, S_m) = \min(n,m)$, $S_n$ is not stationary in the ...
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21 views

Estimation/Calculation of intercept with ARIMA model after differentiating

I am performing regression with ARIMA model because of autocorrelation of my data. My data are the concentration of air in the workplace and gathered by real time monitor with interval of 1 minute. I ...
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27 views

Best way to handle autocorrelation in residuals from panel data regression (FE)

What would be the best way to handle autocorrelated residuals in my panel data analysis (Fixed Effects). What I've tried: -Adding different regressors (no luck there), and besides the current model ...
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24 views

Minimizing the sum of squares of autocorrelation function of residuals instead of sum of squares of residuals

I am trying to fit my multi-exponential model to some experimental data and I am using a simulated annealing algorithm. My objective function has so far been the sum of squares of the residuals: ...
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23 views

R Library for computing cepstral coefficients from Auto-Correlation coefficients

My main goal is to compute cepstral coefficients in R from an ACF vector (Auto-Coorelation function vector with discrete time-step). Correct me if I am wrong in terminology or whatever as I am not a ...
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18 views

Covariance between two sample means of correlated data

I have two sets of random data $X=\{x_1,...,x_N\}$ and $Y\{y_1,...,y_N\}$ both of length $N$. The sets are autocorrelated such that the correlation between $x_i$ and $x_j$ depends only on $|i-j|$. ...
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Can nonstationarity be told from the autocorrelation function?

Here "stationarity" means the first and second moments don't change over time. From a page of Time Series: Theory and Methods, by Peter J. Brockwell, Richard A. Davis In this chapter we shall ...
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26 views

Choosing an autocorrelation structure with negative correlation at last lag

I have a linear model for an experiment using repeated measures. Thus far I've used lme in R to test the model. For this model the the latest lag is 6. The ACFs are: ...
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21 views

Error when using corAR1 and varExp in mutilevel model

I'm using nlme in R to fit a multilevel model for some physiological (skin conductance level) responses while watching a film. I'm specifying the model as: model <- lme(SCL <- variableA * ...
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2answers
80 views

ACF of the errors

For revision, I am working out a multiplicative model for sales data, and then conducting a simple error analysis (actual sales - forecasted). I understand the process but in my lecturer's mark scheme ...
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1answer
59 views

Ljung Box test in R

I'm new to stats. I want to get clarity about Ljung Box test. Its a omnibus test. I'm using R to test autocorrelations of a time series. Using below command ...
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1answer
73 views

Autocorrelation for regression

I am attempting to use a significant autocorrelation (where it lies outside a 95% interval around 0) indicating periodicity of a signal and use it as predictive variable in a regression. If, for ...
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97 views

Autocorrelation and evidence of iid

Suppose I have the first seven autocorrelations for some variable $x$. And suppose they are -0.2, 0.15, -0.05, -0.10, -0.05, -0.14, 0.04 How can this be used as evidence of my data being or not being ...
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95 views

Model estimation - 2sls

Firstly, I am applying a 2sls model in my paper: ...
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62 views

Specifying the correlation structure of an unevely spaced time series in GEE with geepack

I have counts of plants from different sites over a number of years. In each census year, all sites were surveyed, but the gaps between census years vary (between 1 and 4 years between consecutive ...
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126 views

How is the proper number of lags for ACF or PACF displaying?

How many lags should be used for ACF or PACF displaying if we have $S$ seasonality? For example, for 500 observations I have 25 lags for 200 observations I have 22 lags It is independent from ...
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48 views

nonlinear dependence in autocorrelation lagged scatterplot

In lagged scatter Plot we have such a diagramm: if we have an organized curvature in the pattern of dots, that means, nonlinear dependence between time seprated. my question is now: in which time ...
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44 views

What does the theoretical crosscorrelation function look like for two unrelated random walks?

What does the theoretical crosscorrelation function look like for two unrelated random walks? I know that for two random walks, they will be spuriously correlated. But what about the autocorrelations? ...
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197 views

Do autocorrelated residual patterns remain even in models with appropriate correlation structures, & how to select the best models?

Context This question uses R, but is about general statistical issues. I'm analysing the effects of mortality factors (% mortality due to disease and parasitism) on moth population growth rate over ...
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23 views

The “right” HAC

I’m estimating a single equation time series model with yearly data (70 observations). To eliminate or reduce the influence of autocorrelated residuals and to obtain unbiased standard errors, I want ...
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56 views

Dealing with nested factors and correlation structure in a GEE model

This question is of a previous one that has not been answered yet (see the details of our experiment and question here). We are now exploring a GEE (Generalized estimating equation) approach that ...
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1answer
107 views

When should one avoid using Durbin-Watson test for autocorrelation?

Over 60 years ago Durbin and Watson suggested a testing procedure for assessing autocorrelation in regression relationships.The test is known to not work in the presence of lagged dependent variables, ...
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80 views

why sinusoid pattern in correlogram

Why does the ACF of an AR(1) contains sometimes a sinusoid-like pattern? and what does it mean? EDIT I think the time series is fit to AR(1). As I understand it, in an AR model, the value of x ...
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184 views

Which one of these looks stationary?

Step 1. To answer "Final Question" ( linked: "THE FINAL QUESTION : Order of differencing, to achieve stationary and interpretation of arima() , acf, pacf?") Expecting to find correct order of ...
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1answer
119 views

Summing variance of autocorrelated timeseries

Problem: When trying to calculate the variance of timeseries sums I get a negative variance, mostly due to autocovariances at large lag steps. Does not seem realistic. I have a timeseries which is ...
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1answer
61 views

Confidence band in correlogram

Could some one explain me, what is the confidence band in correlogram and if an autocorrelation coefficient is out of this line, what does it mean? For example in my Diagramm, lag 14 is significantly ...
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144 views

Characterizing a time-series using autocorrelation lag values

I am seeking to characterize time-series data (specifically parameters derived from sensor data) for 18 patients collected over 20 days using autocorrelation (see plot below of autocorrelation ...
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70 views

Test for granger causality after fitting a GARCH(1,1)

I have two time series, where i wish to test for Granger causality of lagged values of $x$ on $y$, $y$ is changed to "rate-return" and $x$ is the positive or negative "rate-return", that is everywhere ...
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153 views

Detecting outliers using correlogram

If there is an outlier in a time series, how does its correlogram behave? Is it possible to find outliers using a correlogram? EDIT I have such a Time series: ...