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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Variance of autocorrelation

At this link I have seen the following formula whereas $$ r_k = \frac {\sum_{t=k+1}^n a_t*a_{t-k}} {\sum_{t=1}^n a_t^2}$$ $$Var(r_k) = \frac {n-k}{n*(n+2)}$$ where $r_k$ is the autocorrelation at ...
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Why does first differencing correct autocorrelation?

If we have an autocorrelated variable in the multiple regression model, why does taking first difference help?
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Autocorrelate relative difference between two time series

I would like to verify the similarity of two time series. So far I have resampled and interpolated one time series, so that the two have synchronous time. Next I have computed the relative difference ...
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Weird thing: The larger my lags, the smaller my Ljung Box test p-values

I am doing analysis to a dataset about U.S. Imports of Goods by Customs Basis from China. I deleted the data of the first 5 years, logged the data, and then decomposed it (or ...
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What are the statistical reasons of choosing between a static and dynamic panel data model?

I would like to know more about the relation between serial correlation/autocorrelation and static vs. dynamic panel data models to decide between a static or dynamic model. Currently, I am analyzing ...
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Autocorrelation in Elo ratings

FiveThirtyEight uses the following formula for their NFL Elo ratings: $$ R_i^{k+1} = R_i^k + K \cdot M(z) \cdot A(x) \cdot (S_{ij} - \sigma(x)) $$ where $z$ is the game's margin of victory, $x=R_i^k - ...
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Accounting for spatial autocorrelation in model - A simulation

My question, in short, is: I was trying to demonstrate that accounting for spatial autocorrelation reduces the overestimation of significance of a non-autocorrelated fixed effect. The result, ...
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Problem with Assumptions of Panel data with random effects

I am studying with a Panel data 316 of observations and 73 groups. First, when I examine the homoskedasticity issue, I got following results with df(72,243) by using Levene et al. Test: W0: 2.5 (Pr>F =...
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When to use a Hidden Markov Model vs Markov Model with history?

I'm trying to understand when and why it's useful to use hidden state in a model. The purpose of my modeling is to be able to simulate sequences with features similar to observed data sets. As a ...
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How to specify an autoregressive correlation structure in a linear model when the data has multiple observations at each time step?

I want to fit a multiple regression model that accounts for temporally-correlated errors (i.e., some sort of autoregressive correlation structure, like those provided by ARMA or ARIMA models). However,...
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Defining error safety in cross correlation of two binary signals

I want to cross correlate two binary signals, where one is currupted by noise and shifted by a timeconstant tau, but has the same bit pattern (so basically an auto correlation). Similiar to case 2 in ...
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First difference of AR(1) process

Given AR(1): $$X_t - \mu = \phi(X_{t-1}-\mu) + \epsilon_t$$ where $$ \mu = 0.85 \\ \phi=0.59 $$ and $$ W_t = X_t - X_{t-1} $$ Compute $$ Corr(W_t,W_{t-1})=-0.205 \\ Cov(W_t,W_{t-4})=-0.43 \\ Corr(...
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compare a neighbourhood value with the city mean - test of significance in presence of spatial autocorrelation

I have a dataset with all neighbourhoods in a city and a value for each neighbourhood (a rate). I would like to be able to create a vizualization that enables the user to select individual ...
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43 views

General formula for AR($p$) auto-regressive time series

I'm trying to find a reference (including the full formula) for the following. If $X_n = a_1 X_{n-1} + \cdots a_p X_{n-p} + e(n)$ where $\{e(n)\}$ is a white noise, then $$ X_n=g(e_0,e_1,\ldots,e_n)+\...
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Multivariate normal error with autocorrelation in second dimension

I am trying to forecast my model, but am unsure how to so in terms of error distribution (using mvrnorm). The model itself essentially estimates numbers over time and state (a matrix time x state). ...
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How do I read an auto-correlation plot?

I'm taking a data camp lesson by Professor Rob J Hyndman. He went over the ACF plot and said that you know the period of seasonality based on the highest point in ...
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Nonlinear Regression with Correlated Error

Assume I have two data sets: Experimentally measured data y for known values $x$. Assume the nature of the error in $y$ is random only and $\sigma_y$ is known/estimated. Simulated (deterministic) ...
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Sample autocorrelation of random walk with drift

I would like to calculate the autocorrelation of a sample whose data generating process is a random walk with drift. I generated the movement over 250 time points of a fictious stock price with ...
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why would do (F)GLS and multilevel modeling simultaneously?

To my knowledge, we could develop a multilevel model if we have a data that has a clustered structure in order to adjust for the auto correlation happening within each cluster. Then, we also learn ...
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How to estimate ARIMA parameters for the set of time series

If I have a set of time series. For example orders of the users. How.can I estimate best p and q for the whole dataset not just one user history
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Durbin-Watson Test and p-value

What should I do if the p-value in Durbin-Watson test is zero (using R)?
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Eviews- Error correction estimation using BDM's one-step procedure

I am trying to estimate an equation for the average wage using quarterly data. I want to build an ECM which can bes estimated using Banerjee-Dolado-Mestre's approach to cointegration. So far, I haven'...
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What is the difference between an AR process and autocorrelation?

Or is it maybe the same thing? I see that autocorrelation is when Yt is correlated with its lag Yt-1. But isn't that essentially what an AR process (say AR(1)) is? We are assuming that there IS ...
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42 views

Use cor instead of acf function?

I would like to have the same results using acf() function and cor() on a very easy ts. Unfortunately I am not able to. I ...
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Significance of the autocorrelation for repeated measures

For example, I perform the following experiment: I invite the person and instruct him to stare on some object for 10 minutes. During this trial, I detect blinks and measure inter-blinks intervals (...
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Checking auto correlation and cross-sectional dependence of a variable

I have a variable consisting of a sample panel of 500 ids and 120 timestamps. I want to assess whether there is any auto correlation and cross-sectional dependence for this variable. Please suggest ...
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Misunderstanding of time series autocovariance

I'm reading the "Time Series: Theory and Methods (2nd ed.)" by P.J.Brockwell and R.A.Davis. I've stopped at the one moment at pp.218-219 (Chapter 7 "Estimation of the mean and the Autocovariance ...
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Power law vs exponential law decay autocorrelation function. What is the difference

Once I read that it is possible to speculate about decay type of the autocorrelation function (ACF). Unfortunately, I forgot the link and main idea. It sounds like if ACF decay is exponential, then my ...
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Is the stationarity property invariant by transformation?

In other words, if $X_t$ is $I(0)$, is $f(X_t)$ also $I(0)$? I would say yes: The mean stays constant. The autocovariance still depends only on the lag between the terms.
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Including time variable as a fixed effect to get rid of autocorrelation?

Does it make sense to include time as a fixed effect along with your predictors to get rid of autocorrelation? Why or why not?
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58 views

Significant lags at ACF and PACF plots in GLM: what should I do?

A glm.nb model I built shows significant lags at lag 1 in both ACF and PACF plots. Please see the images below. There is no way to define random effects (or ...
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Why does the correlation function of this stochastic differential equation starts at different points?

I am working with the following differential equation: The equation is $$x=\beta +\sqrt{2D} \xi(t)$$ where $\xi(t)$ is a white noise term, with a reflecting wall boundary conditions. After solving ...
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What do my first difference ACF/PACF show me? [closed]

I am quite new to econometrics, so not sure how to intepret the following acf/pacf function on log financial time series after first differencing; The level data showed a AR(1) process, how would I ...
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Durbin-Watson test and coefficient significance yield different conclusions?

I'm not sure where my confusion is stemming from, but it seems that equivalent tests (Durbin Watson, and a simple significance test) for serial correlation in the errors (of lag 1) sometimes yield ...
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finding regression coefficients and deviation with autocorrellated outlaws

I try to make regression analyses to vector of average month C02 concentration in the air. ...
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52 views

How can I test for autocorrelated errors in logistic regression?

I'm doing a Bayesian logistic regression $Y \sim X$ where my predictor $X$ is a count observed over time. So $Y$ and $X$ are each $m x n$ matrices where $m$ is the number of subjects and $n$ is the ...
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Autocorrelation of stochastic process with python

So I am trying to simulate a SDE and find the corresponding correlation function. The equation is $$x=\beta +\sqrt{2D} \xi(t)$$ where $\xi(t)$ is a white noise term. After solving it using Euler-...
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Ljung-Box Test in finite sample proof [duplicate]

Initially I have seen that in order to analyze residuals for finite sample, Ljung - Box is defined as $n(n+2) \sum_{n=0}^h p_k^2/(n-k)$ where $n$ is the sample size, $p_k$ is the sample ...
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ACF and PACF Interpretation 12 month difference/seasonality

Looking for help interpreting the following ACF and PACF plots, for a time series SARIMAX model analysis (p,d,q) and (P,D,Q,12). I have searched online and have not found an example that explains it ...
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How to adjust for spatial autocorrelation in panel regression in R

I am running a panel regression with two-way fixed effects, the outcome variable being the number of conflicts in each district each month. My calculation of Moran's I seems to indicate that the ...
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Distribution of sample variance for dependent variables

In several references I have found distribution of sample mean $\hat{\mu}$ for dependent data. Here, for example. But can someone give expression (preferably with derivation) for distribution of ...
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203 views

Calculate the autocorr. function of ARMA process

I'm new to time series. I would like to calculate this.. but I really don't know how to begin... ARMA(1,2) $X_{t}=\underbrace{\phi X_{t-1}}_{AR(1)}+\underbrace{\epsilon_{t}-\theta_{1}\epsilon_{t-1}-\...
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ARIMA Model Ljung-Box Test Derivation

Initially I am aware of the fact that in order to analyse autocorrelations of residuals of ARMA(p,q) we apply Ljung-Box test and involve chi-square distribution (because autocorrelations are ...
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190 views

Fixed effects - correcting for autocorrelation and heteroskedasticity, panel data analysis in R

I have a datset of 25 counties over 11 years, with response variable unemployment ( in %), and 6 explanatory variables (proportion with high school, some economic indicators, etc). After some tests ...
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Type 2 error in t-test on time series

I have an AR(1) time series with $1>\phi>0$. If I naively use t-test to check $H_0:\mu=0$ and it does not reject the null, then can I accept the result? I think yes because for a time-series ...
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How to deal with circular causality

Often in time series and panels, the "dependent" and "causal" variable don't share purely that relationship. There is a fair bit of reverse causality as well. ,e.g. x causes y, but then either y ...
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Vector Autoregression - How do we choose the correct value of p?

I am following this article: https://otexts.com/fpp2/VAR.html#fn24 ...
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DW critical value for more than 200 sample

does anyone know what is the dU & dL value in DW test for 252 sample? And how to calculate the DW critical value in Ms Excel? In ref., i only found for less than 200 samples. I need your help guys,...
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Correlation of time series with auto-correlation

When we calculate the variance of a auto-correlated time series, we need to do some shrinkage to get the correct value. What about say we have two time series, X, Y. Each has auto-correlation. Will ...
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46 views

How to calculate the lag of a prediction of a time series?

I am trying to learn a time series (Mackey-Glass) using a neural net. In order to see if there has been success in the learning process, I am looking at the correlations between the predicted and real ...