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Questions tagged [autocorrelation]

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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What does it mean that if distr. of $X_j$ does not depend on $j$, $E(X_j)=\alpha$, then $Cov(X_i,X_j)$ dep. only on $|i-j|=:d$?

What does it mean that if distr. of $X_j$ does not depend on $j$, $E(X_j)=\alpha$, then $Cov(X_i,X_j)$ dep. only on $|i-j|=:d$? $Cov(X_i,X_j)=E[(X_i-E[X_i])(X_j-E[X_j])]$ $=E[(X_i-\alpha)(X_j-\alpha)...
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What causes the degeneration of correlation in a simulated time series?

I am trying to simulate an ARMA(1,1) process with the following characteristics: $\phi$ = 0.97 $\theta$ = 0.80 Standard deviation $s$ = 245 Mean $m$ = 1000 ...
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why does ignoring spatial autocorrelation lead to spurious significance

In spatial statistics one often hears the statements like the following: unaccounted for spatial autocorrelation may lead to spurious significance / understimated uncertainty / too narrow ...
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Autocorrelation: Multiple observations at lag 0

I have data recorded over 100 days. For each day there are ~5-10 observations. How can you check whether residuals of one day are correlated at lag 0? More precisely: Are residuals of the same day ...
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Cross Correlation between two RVs and PCA

What is the difference between the maximum value of cross-correlation value of RVs X, Y and maximum eigenvalue of Covariance matrix of these same RVs X and Y? Are both same and just represents the ...
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When can Autocorrelation of Residuals be ignored?

One assumption of OLS regression is that residuals are idependent, so that there is no autocorrelation. When I checked the assumption, I noticed that autocorrelation is present. Now here are two ...
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Stationary processes that do not satisfy Gordin's central limit theorem

We are doing an assignment for our Advanced Econometrics course for which we are trying to illustrate Gordin's Central Limit Theorem by simulation. We used an AR(1) process to show that if the ...
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How much Autocorrelation is acceptable in Regression Analysis?

One assumption of regression analysis is independence of residuals. I checked this assumption and found small autocorrelation (see figure). One remedy would be to incroporate dummy variables for the ...
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In OLS, is autocorrelation/serial correlation still an issue when both regressor and regressand are time series data?

Suppose I am trying to figure out the slope between Jet Fuel and Brent Oil Index to hedge for price movement in Crude Oil, and say I have the following data available: Monthly Ending Price such as ...
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Abbreviations: StatsModels handling NaN

In StatsModels there are keywords to specify how to deals with NaNs. 'none' := no checks for missing values 'drop' := drops missing values 'raise' := raises an error But there is another keyword: '...
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Autocorrelation with missing Data

How should missing observations be handled to create ACF-Plots? Let's assume we have a time series t = [1, 1, 1, 2, NaN, 3, 2, NaN, ...]. What schould be done with these missing data points? I have ...
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How to show random sampling implies no serial correlation in errors, so OLS assumption with no serial correlation is fulfilled

I am trying to prove the given random sampling, the $Cov(u_{i}, u_{j}) = 0$. Here is my prove: Assume given $y_{i}, y_{j}$ with random sample, where $y_{i} = \alpha + \beta x_{i} + u_{i}$. Also ...
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Dealing with autocorrelation using Generalized Least Squares

I have a time series data set where the auto correlation of the residuals follow an exponential decay. I was wondering how I should deal with this? I would like to fit a linear model and have tried ...
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Can someone help me to interpret these autocorrelation plots?

I've got these two acf plots that were produced in R. The first plot is the acf of a differenced time series (in this case tweets from twitter). The second plot is the acf of the remainder component ...
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Autocorrelation in a subdivided unit of analysis [closed]

Sorry if this is awkwardly worded...I'm not sure how else to describe my question. I have 4 "experiments" containing 3 "duplicates" with 28 "runs" in each. Each run is a time series of 300 seconds....
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Autocorrelation, trends and lag

The following graph shows detrended data from a time series. Autocorrelation has been performed in MATLAB software using a lag of 999 (because there are 1000 data points). This is the maximum allowed. ...
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Contradictory Ljung Box results

We want to apply extreme value theory to the maximum yearly temperatures. Before we choose the model we want to test whether or not we can assume independence. First we made a plot of the ...
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Autocorrelation and Lag

How do I interpret this autocorrelation and partial autocorrelation graph?
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why fit `ARMA` model to residuals when doing residual analysis?

I started my Time Series Analysis not long ago and I am currently at the residual analysis. I found, in the course, the tutor was demonstrating residual analysis by fitting an $AR$, then $ARMA(p,0,q)...
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No autocorrelation in time series

I am trying to predict a time-series data set, using python. I have a timestamp and number of calls in a network for this particular timestamp. I have to predict number of calls in the future. ...
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Projection in AR model

I am currently reading the Brookwell and Davis Book and cuurently read about the PACF. On page 98 they derive the PACF for the AR(1) model $$ X(t)=0.9X(t-1)+Z(t) $$ and say that the orthogonal ...
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Interpreting autocorrelation in time series residuals

I am trying to fit an ARIMA model to the following data minus the last 12 datapoints: http://users.stat.umn.edu/~kb/classes/5932/data/beer.txt The first thing I did was take the log-difference to get ...
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Mediation analysis with depent observations. Is it possible with mixed models?

I wonder whether it is possible in principles to conduct a mediation analysis with dependent measures. The problem is of course that we are violating the assumption of independence of observations. ...
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Autocorrelation in glm.nb with one variable

I have made a model of parasite infection intensity and my model is autocorrelated even though I have only included one variable. The initial model looked like this: ...
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Autocorrelation Functions/Autocorrelograms and the assumption of Weak Stationarity?

Does it make sense to even speak of the autocorrelation function or of the autocorrelogram for a non-weakly stationary series? Anytime we see an autocorrelation function or an autocorrelogram can we ...
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Why to use ARMA model as a time series is either over-differenced or under-differenced?

Knowing that a time series is over-differenced or under-differenced, and adding an AR term to the model means that we are partially differencing the time series if it's underdifferenced till a white ...
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Time Series ARIMA gives similar result for different parameters

While learning TimeSeries modelling... I saw statsmodel.tsa.Arima_model.Arima result for following 2 sets of parameters (0,1,0) and (0,2,1) where the order is(AC, Difference, MA). When i used above ...
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Fitting an ARMA-GARCH using AIC

I am trying to fit an ARFIMA(p,d,q)-GARCH(1,1) model to an asset returns time series. I start with an ARFIMA(0,0,0)-GARCH(1,1). The diagnostics tests like persistence requirement, Ljung Box test for ...
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Autocorrelation with Replicates

How to perform autocorrelation with replicates? For each day I have many observations and I want to check wether these observations are correleated with the next day and the day after this day. If if ...
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Vector ARIMA residual testing

I wonder how testing the residuals of an ARIMA model works when it comes to vector ARIMA models. Can I simply take the residuals of each univariate estimate and test them seperately for ...
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Independence of Residuals: Multiple Measures for each Point in Time

One assumption of OLS regression is independence of residuals. I'm not sure how this assumption can be checked for the following study design. Every day 5 measurements were carried out, for which I ...
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Spatial autocorrelation and predictive accuracy

Hi everyone! I have a training dataset of observations from nine river sites relating three predictors and one (known) response variable (K) and I am testing several algorithms (boosted regression, ...
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Automatically calculating standard error of auto-correlated time series

From molecular dynamics I get different time-series with varying autocorrelations. Is there a way to directly calculate standard error ($\sigma/\sqrt{N}$) for such autocorrelated data? I don't want to ...
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1answer
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Autocorrelation in a predictor variable

Suppose that my main purpose is to model (using GLM e.g.) an annual count data by using two predictors one of which is mean annual water level measurement which, in itself, is auto-correlated (i.e. ...
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Modeling quarterly default rate (non stationary, autorregressive time series)

I am a student writing my thesis on default rate modeling. My major is finance, so I'm not really experienced in econometrics. I'm trying to create a model for quarterly corporate default rates (...
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Why are Gaussian Processes valid statistical models for time series forecasting?

Duplicates disclaimer: I know about the question Time series forecasting using Gaussian Process regression but this is not a duplicate, because that question is only concerned with modifications to ...
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How to properly utilize lag and errors in Time Series modelling

I have a dataset of 2 variables that should be heavily correlated. There are some underlying reasons why this set has an R^2 of only 0.620 when modeled in a simple Linear Regression; the independent ...
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Imposing independence constraints in mixture modeling of correlated data?

For 1-D signals (spectra) or 2-D signals (images), is there a way to impose the constraint that the data within a group is uncorrelated? I am iteratively applying background correction model fitted to ...
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VAR model residual autocorrelation and variable selection

I have a question on VECM model. I have a set of variables I had planned to include in my VECM model where one particular variable may be trend stationary (@ 10% s.l. by ADF test) while the rest are ...
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What methods can be used to select the lag variable for a multivariate time series?

I have a time series, it looks something like this (where X are the predictors and Y is the output variable): ...
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1answer
47 views

can a vector of strictly positive values have a negative autocorrelation at any lag?

matlab is giving some weird results. I have a vector of nonnegative numbers which is the duration between subsequent events. I calculate the autocorrelation of this and plot it, and after about lag ...
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Is it possible to generate a correlated discrete binary sequence given an arbitrary auto-correlation function?

If we know $\phi_{XX}$ of a Discrete random variable ${X}$ can we generate a sequence of samples whose autocorrelation $\tilde{\phi_{XX}}$ approaches $\phi_{XX}$? I ask this in the context of ...
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Inconsistent autocorrelation plots

I used pandas.tools.plotting.autocorrelation_plot in Python to plot autocorrelation functions of the same time series: for its first 100 and 1000 entries, respectively (code below). ...
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Autocorrelation with additional binary predictor

I have the data in the following format: ...
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32 views

How valuable is a regression result with serially correlated residuals?

I performed a linear regression with two time series variables. First, I checked stationarity of both time series via ADF/PP/KPSS tests and all three indicated non-stationarity. However the test of ...
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1answer
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Is ACF plot enough to rule out auto-correlation in my model?

Do you think it's enough to check ACF plot to rule out possibility of auto-correlation in the data?
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Positive lag-1 autocorrelation after differencing a stationary time series

In the following post it is trying to explain why the lag-1 autocorrelation is negative after first differencing a stationary time series. Why does differencing time-series introduce negative ...
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Autocorrelation in loss function, want to perform DM test. How many lags to use? (R)

I have two sets of forecasting errors, and want to perform a DM test. Both forecasts are a fixed size moving window, and are 1 day ahead forecasts. The first step of performing the DM test is to ...
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1answer
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What can we predict from the follow ACF and PACF plots?

This is a time series of a wind speed data collected every hour for a month. What can you interpret from the ACF and PACF plots about the trends and seasonal components? Are there any? And which model ...
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