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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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How can I map a Gaussian vector according to an equation that has a spatial autocorrelation function?

I have the following function: $E(x,z)=30-0.5z+12.5\frac{e^{Y(x,z)}-e^{0.5}}{\sqrt{e^2-e}}$ I want to run some Monte Carlo simulations and at each simulation I have to generate values for $E$ at ...
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Autocorrelation in residuals

Hi guys, thanks for your time! Problem description: I am working with dynamic factors. I have 4 panels of 24 series (hourly electricity prices) and I reduce them to 1 dynamic factor each that I then ...
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Arima with multiple autocorrelation coefficients [on hold]

I am new to time series analysis. I want to know that if it is possible to build an ARIMA Model with multiple p-values taken at once. I mean, if time series is related to multiple time lags, in that ...
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Best way to measure reliability of auto-correlated data

I'm trying to compare different ambulatory devices for measuring heart rate against a gold standard in-lab assessment. What is the best way to determine whether a device is worth using. I can use ...
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Confidence interval of mean for time series

I have data from a humidity sensor and would like to estimate the confidence interval of its mean value. However, since the time stamps are "too close together" the data-points are correlated. ...
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temporal autocorrelation machine learning algorithms

I am trying find out the relationships of stream integrity against Land uses. I have 4-years of stream integrity data (1998-1999, 2004, 2009, 2014) and corresponding land use data of 1995, 2002, 2007, ...
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How to define Autocorrelated Copula?

I want to make a copula between two auto correlated timeseries.Since it would be better for the timeseries not to be auto correlated, was thinking about making ARIMA (Autoregressive Integrated Moving ...
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Stationarity test for autocorrelation

can we use unit root test of residual to detect autocorrelation in a time series model? Are stationarity of the residual means there is no autocorrelation?
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How to ensure independence of calibration and validation data a spatial model considering spatial autocorrelation?

I determined the vegetation type (4 types all in all) at 120 points (stratified random sampling) in my study area (650ha). I want to use the points to train a statistic model (eg. random forest) based ...
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Are Poisson Regressions with Serial Correlation Biased or Inconsistent? (No Fixed Effects)

Let's say I've got panel data where a count outcome $y$ and continuous independent variable $x$ observed each time period $t=(1,2,...T)$ for each individual $i$. I am interested in how $x_{it}$ ...
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Am I doing the correct data transformation for Granger causality tests

I have seven sets of time series, below is my process flow, am I doing the correct thing here? especially step 4. Raw data transform and test stationary with unit root test (ADF), with level, first ...
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Should I use weekly or daily returns for modelling FX returns?

I am currently modelling Foreingn Exchange returns using a GARCH model. I am simulating returns 1-year forward. Would it be better to use weekly or daily data on Foreign Exchange returns? Weekly data ...
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Identifying autocorrelation / serial correlation from graph?

I'm new to statistics and I'm currently working on some exercises to identify serial correlation visually. This is from a time series exercise of Dollar-Pound Exchange Rate. After running a simple ...
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definition of integrated- and- exponential autocorrelation time

I understand them (to an extent) both seperately, but i was reviewing my notes from class and my verbal definition is effectively stating the same thing in different words. I have: integrated: ...
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Should the autocorrelation time drop after many steps or converge to a fixed value?

I'm using Bayesian MCMC to explore a 6 parameters model (the parameters are quite correlated). In one of these runs, I noticed that the estimate of the mean (across chains and parameters) ...
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How can I find a representative point in 3D matrix (time,lon,lat)

I have temperature in a matrix of time, longitude and latitude. I need to find a way or criterion to find a point or location (lon *, lat *) that is representative of my entire area of interest (time, ...
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Large N Large T Unbalanced Panel - Serial Correlation

I have an unbalanced panel data, which consists of 180 vintage groups. The ith group will have time series length of t=181-i. For example, Group 1 will have 180-month observations; Group 2, originated ...
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How can you test dependence for non-Gaussian standardised residuals?

Let's say you fit an ARMA-GARCH model to financial data and find that the standardised residuals are non-Gaussian through the Kolmogorov-Smirnov test. These residuals have mean -0.002 and standard ...
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Moving Average Representation of a Stationary Time Series

I was wondering if this equation is considered a Moving Average process of order 13? If so, does that mean that the coefficients at times t-2 to t-11 are 0? As they are clearly not present in this ...
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Model selection with different fixed effects and different corARMA structures

I analyzed the effect of temperature (4 different areas) on laying date: LDT ~ Aa3+Bb+Cc+Dd. Because of autocorrelation in residuals I used ...
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Expectation, variance and autocorrelation of a “complex” AR(1) function

I'm preparing the exam for "stochastic models" and I encountered this exercise which is giving me a lot of problems: Let $$X_t=\phi X_{t-1}+\epsilon_t, ~~~~~~~~~~\epsilon_t \sim WN(0, \sigma^2)$$ ...
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Inverting MA(1) to AR(Inf) [duplicate]

While it is $MA(1)$ process there is no dependence between $u(t)$ and $u(t-1)$ i.e $$u(t)=v(t)+Q(1)v(t-1)$$ but when i converted it to AR process i get $u$’s that is dependent on the other $u$’s i.e. $...
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How to deal with auto-correlation in generalized linear modelling?

I've built a generalized linear model by using glm.nb function (my response is a count type of data) using a single predictor. The model summary is given below. <...
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High Autocorrelation - Low Partial Autocorrelation Interpretation

According to the above autocorrelation plot, my time series reaches levels of 20% autocorrelation with certain lags. However, when I plot the autocorrelation and partial autocorrelation, I am ...
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Cluster-robust standard errors in panel data analysis

In a simple panel data analysis with data on 64 firms over 8 years, I use cluster-robust standard errors (at the firm level) to evaluate significance of coefficients. I observe important differences ...
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Returns correlated, but squared returns not correlated [closed]

I'm trying to apply a GARCH model to a financial time series, and as usual I plotted the ACF and PACF of both returns and squared returns. In my time series the returns show serial correlation, but ...
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How to study auto-correlation of time series when shocks are present?

The time series I want to model has several shocks due to law changes. Basically, I do not have a lot of data that isn't impacted by these shocks/shifts/pulses. Now, I want to study the ACF and PACF ...
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Metropolis-Hastings algorithm for autocorrelated data

I have auto-correlated data and I wish to apply the Metropolis-Hastings algorithm on it. The data was obtained by simulating the time evolution of a system, and computing the values of some magnitude ...
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1answer
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Confidence interval with ols and hac

I have to build a confidence interval using OLS and one using HAC (heteroskedasticity and autocorrelation consistent). Which of the 2 ignores the auto-correlation between the errors?
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Autocovariance and autocorrelation function of AR(1) process

I'm preparing the exam about AR models, precisely I have this exercise which I have some issues with points "d" and "e". My try was: Knowing that $W_t=X_t-X_{t-1}$, $h=1$ so: d) $\gamma\left(1\right)...
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1answer
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To standardize or not to standardize in cross correlation

I am new here. My question is simple. Why doesn't the definition of cross-correlation between two time series include a mean centering? Wikipedia defines the cross correlation of two functions as the ...
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Validity of Fisher transformation on autocorrelations?

I'm doing some analysis in which I have to determine if the autocorrelation in one sample is greater than that of another sample. Someone suggested I use the Fisher transform for this purpose, but, ...
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Generate an autocorrelated Gamma sample of length N

How does one simulate an autocorrelated Gamma sample of length $N$? All I found online was about generation correlated variables and not an autocorrelated sample.
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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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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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1answer
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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 ...