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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 are the effects of autocorrelation on logistic regression?

I need a simple way to estimate the probability of winning an auction as a function of bid amount. I modeled the auction using the LogisticRegression from pandas, ...
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Poisson Regression with Temporal Autocorrelation [on hold]

Wondering if it is possible to specify temporal autocorrelation in the covariance structure (specifically AR1) while using poisson regression in R. In the Zuur 2009 book the authors state "However, ...
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Population autocovariance goes to zero, assuming covariance stationary

In time series context, let $\gamma_j=E[(y_t-\mu)(y_{t-j}-\mu)]$ denote population autocovariance, where $\mu$ is population mean of $y_t$, assuming covariance-stationary. Then, $\gamma_j$ goes to $0$ ...
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Sum of autocovariances for AR(p) model

Suppose I have the following $AR(p)$ model. $$X_t = \sum_{i=1}^{p} \phi_i X_{t-i} + \epsilon_t\,, $$ where $\epsilon_t$ has mean 0 variance $\sigma^2$. I am not interested in fitting this model, but ...
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59 views

What model would you suggest for this?

I have been trying to understand what model i should fit to these... I find it hard to understand the shape of ACF. What ARIMA(p,d,q) model is suitable for this data? THANKS... :)
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Correcting or Adjusting Binomial Test for Temporal Autocorrelation

Is there a relatively standard approach for adjusting or accounting for autocorrelation when conducting the large-sample approximation version of the binomial test? I have an equally-spaced timeseries ...
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22 views

Does it make sense to analyse an autocorrelation matrix with Random Matrix Theory?

I wonder whether you can gain valuable information about a time series by analysing its autocorrelation matrix using RMT. I know that RMT can help to extract information about the collective ...
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Definition of the integrated autocorrelation time

Let $(\Omega,\mathcal A,\operatorname P)$ be a probability space $\pi$ be a probability measure on $(\mathbb R,\mathcal B(\mathbb R))$ $(X_n)_{n\in\mathbb N}$ be a real-valued stationary stochastic ...
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How to deal with autocorrelated residuals from a GARCH model?

I am performing GARCH model on some log returns $r$. If time series of $r$ is autocorrelated, I explicitely model it through a AR model. Then I want to perform the GARCH on the same time series: I ...
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25 views

Is it neccessary to test for serial correlation in a multi-level model

I am running a multi-level model looking at factors that explain attainment. There are pupil- and school-level predictors, and the school the pupil attends is modelled as a random effect. I have run ...
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After using spatial regression model, how to test if residuals are not spatially autocorrelated?

I'm trying to perform a regression analysis on spatially correlated data. I performed a linear regression, then tested the residuals using Moran's I, and found that the residuals were spatially auto ...
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How to incorporate AR(1) term in a multiple linear regression model

I was trying to model fish catch (CPUE) using a combination of some categorical and numrical predictors. I have the data for 10 years. The data has been collected only in the period from June to ...
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32 views

What does a “symmetrically grouped” lag plot tell about the data?

I am trying to do time series forecasting on different data sets. I created a lag plot on each set and received an unusual, 'symmetric' but grouped pattern: I would say that this implies a lack of ...
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How can I test if a permutation hypothesis test produces valid results based on the probability distribution used?

I'm using the Join Count statistics to get insight if there is spatial autocorrelation in a categorical feature. I would like to test if the pseudo p-value returned comes from a valid hypothesis test ...
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21 views

cross correlation of series with different event times

I have multiple stochastic processes that emit a signal after a certain waiting time. That signal falls within a range [-n;-n+1;...;n-1;n]. Putting this in a dataframe this would look like ...
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“Regression to the mean” versus serial correlation

“Regression to the mean” says that higher pre-test values will have lower post-test values (and vice versa). This phenomenon will decrease the correlation between the pre- and post-values. However, ...
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57 views

How should I interpret a symmetrical autocorrelation plot?

I have plotted a time series using pandas autocorrelation_plot and mathplotlibs acorr. Notice that the above mathplotlibs image is symmetrical, what would this mean?
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Show autocorrelation at lag 1 for differenced series

Do you know any reference or how to prove that the autocorrelation at lag 1 for differenced series can't be greater than -0.5. This has a link with Why does differencing time-series introduce ...
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Mean and Correlation of a First-Order ARCH(1) Process

For a first-order ARCH(1) process $$ Y_t = \epsilon_t(\alpha_0 + \alpha_1Y_{t-1}^2)^{1/2} $$ $$ t \in \mathbb{Z} $$ $$ \alpha_0, \alpha_1 > 0 $$ $ \{\epsilon_t\}_{t \in \mathbb{Z}} $ and $Y_t$ is ...
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1answer
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Showing the covariance and autocorrelation functions of a stationary time series are symmetric around 0

I need to show that the covariance and autocorrelation functions of a stationary time series are symmetric around zero. From my understanding, this entails $$ \gamma(h) = \gamma(-h) $$ $$ \rho(h) = \...
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1answer
32 views

Mean + Variance/Mean ~ 1 for 70 different (Poisson Distributed?) time series variables

I am working with a dataset from my job which is the number of "events" that occur at 70 different locations on a daily basis, over 964 days. So I have univariate panel data. I imagined each location ...
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Confidence intervals for autocorrelation function

Given a time series data sample I have computed autocorrelation coefficients for various lags, the result looks something like this How do I compute the confidence intervals around the sample ...
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Spatial regression with overlapping areas

Is it statistically correct to calculate a regression with overlapping areas? I have market areas as the spatial unit with different sociodemographic and (macro)economic variables and I´m examining ...
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1answer
28 views

Autoregression in nlme - undestanding how to specify corAR1

I have a dataset of 12 days of diary data. I am trying to use lme to model the effect of sleep quality on stress, with random intercept effects of participant and ...
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How to choose the correct sample and hypothesis test for spatiotemporal observations?

Consider the following scenario: There exist $N=10$ participants in a study. Each participant $i$ is monitored under baseline conditions and later under experiment conditions. That is, the baseline ...
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Determining autocorrelation within occupancy covariates in R

I am doing a study underpinned by an occupancy modelling framework in R using the unmarked package to investigate the influence of different anthropogenic ...
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How to generate synthetic data with specific spatiotemporal correlation

My dataset represents a field evolving over time, so has dimensions [X,Y,T]. I would like to generate synthetic data with the same autocorrelation structure and spatial correlations as the real data (...
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Monte Carlo Metropolis: Standard Error and Acceptance

In a time series data generated by Monte Carlo Metropolis algorithm, when is the standard error (correlation between two data points is assumed to be negligible) is higher - when the change in the ...
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When to address spatial auto-correlation?

I am trying to understand when I should address spatial auto-correlation. Let's say that I have a number of weather stations in the mountains and an equal number of weather stations by the sea. I ...
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What is the meaning of having the autocorelation function a cut of at a specific lag and at the same time the partial autocorrelation tails off

having the case that the ACF have only, for example on spike at lag 1 , and the PACF decays exponentially this is a MA model signature. but what is the meaning of having the a value at a the lag K on ...
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More AR lags means more persistence?

Suppose that $x_t$ is an ARMA(p,q) stochastic variable and that $y_t$ is another stochastic process that satisfies $$ y_t = \frac{1}{(1-\rho_1 L)\cdots(1-\rho_n L)} x_t, $$ where $L$ is the lag ...
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TimeSeries Analysis for a dataset gave different result for a calculared subset of it

I am trying to understand timeseries analysis. I ran ARIMA model for same, the values i got were... p,i,q =(7, 1, 1) Now i created a subset from this dataset by applying certain external filters ...
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Variables of interest in regression are different manipulations of same time series data - is collinearity a problem?

I am working with time series data and would like to test two different forms of operationalizing patterns in these data. I am specifically interested in a measure of instability (specifically mean ...
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28 views

How to test autocorrelation

I have the following time series data: 0.9803921569 0.9166666667 0.9090909091 0.8571428571 1.4915254237 0.4059620015 I want to check how correlated these data ...
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Linear model from iterative process in R

I would like to test a relationship between to factors such as birds occurrence and temperature for instance, to test if temperature affects birds occurrence from a country (e.g. Germany). I have a ...
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Moran`s I interpretation

Could you please help me with interpretation of Moran`s I results (two cases). First I have a sample of 373 objects, based on their coordinates I created in R distance inverted matrix. The code to ...
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Identifying ARMA model

In "Time series analysis with applications in r Jonathan D.Cryer and Kung-skit Chan" Hannan and Rissanen proposed getting the time series order by 2 steps which are (chapter 6, section 6.5): 1-Fitting ...
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Why is correlation proportionate to the area of the intersection of the areas under the curves of the series?

I've been staring at this diagram from Wikipedia, trying to understand (particularly autocorrelation): I see that the autocorrelation seems to be proportionate to the overlap between the graphs of ...
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Cross correlation looks like an autocorrelation

I am cross correlating ambient noise data from stations that are 10km apart. The output was an autocorrelation instead of a cross correlation. What could be the reason for this?
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Standard deviation of standard deviation of autocorrelated timeseries

I'm trying to get an estimate of the error in my sample standard deviation (not a statistician at all, hope I'm using correct terminology). The timeseries is normally distributed and follows an AR1 ...
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High correlation between $y_t$ and $y_{t-1}$ makes $x$s insignificant in regression

I want to estimate the following cross-sectional regression: $$y_t =\alpha +\beta_1 x_{1, t-1} + \gamma'X_{t-1} $$ where $y_t$ is my dependent variable and $x_{1t-1}$ and $X_{t-1}$ is a matrix with ...
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Clustered standard errors vs. serial correlation

I have a probably simple question but I can't find an adequate answer. I have self-collected data from three monitors that measure temperature, humidity etc. I useed all three monitors simultaneously ...
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How to reduce autocorrelation in MCMC

I'm using MCMC to simulation the distribution of some parameters in a Bayesian hierarchical model, which has the following form: $$\gamma_{ik} \sim Ber(\omega_{ik}).$$ Then I make a logit-...
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Regression of cointegrated variables, serial correlation

I have a response variable $Y$ and a series of predictor variables $X_1, X_2, ... X_n$. All are $I(1)$. I found that $Y and X_1, X_2, ... X_n$ are cointegrated. To estimate coeffcients of $Y ~ X_1,...
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Autocorrelation, Autocovariance and Large lag Standard Error

I have time series generated data from Monte Carl-Metropolis Simulation. I have estimated correlation coefficients using: $r_k = \frac{c_k}{c_0}$ where $c_0$ is the varaiance and $c_k = \frac{1}{N}\...
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How to interpret autocorrelation plot?

I'm having trouble making sense out of this ACF plot According to an ADF test, the series is definitely stationary. Also, the presence of autocorrelation is explained by the order 1 lag, as evidenced ...
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Standard Error in Auto correlated Data

I have time-series data generated via Metropolis algorithm - Monte Carlo simulations. Since these data must have some correlation between them, the formula of the standard error for IIDs variable must ...
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How do I treat a seasonal timeseries to get a white noise autocorrelation plot?

I have a timeseries which is clearly seasonal and has trends. I would like to treat the data (e.g. differencing), to get a white noise autocorrelation plot. Here is the autocorrelation plot for the ...
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Classification of temporal correlated data in out of fold prediction - Surprisingly high Accuracy

At the very moment, I might have awesome results or a problem. I will start with an overview about my problem setting. I have temporal correlated data (~10000 observations, ~200 features) from two ...
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Time Series Extrapolation from existing past values

Using the Levinson-Durbin algorithm, I am trying to predict the next value in a time series based on previous observations, but the results do not follow the trend of the time series. How can I ...