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Questions tagged [autocorrelation]

Autocorrelation (serial correlation) is the correlation of a series of data with itself at some lag. This is an important topic in time series analysis.

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Can Autocorrelation be used to Differentiate Signal Quality (High, Medium, Low, Very Low) for Periodic Signals?

I'm working on a project to classify the quality of periodic signals into four categories: high, medium, low, and very low (noisy). I was initially exploring autocorrelation as a potential feature for ...
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Autocovariance of the product of two time series (not necessarily independent, uncorrelated or multi-variate gaussian)

I am working with time series that are the product of two other time series that may be related to one another so. In each case: \begin{equation} f_t = x_ty_t \end{equation} and I want to find the ...
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Alternative method to deriving autocorrelation function of stationary AR(2) process [duplicate]

I have read this question/answer: Autocorrelation of a stationary AR(2) process How can we derive this using Expectation. Let $Y_t = \phi_0 +\phi_1 Y_{t-1} + \phi_2 Y_{t-2}+\epsilon_t$ I found the ...
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Is it possible to control for autocorrelation within individuals and families using GLS corCAR1?

I have a sample of twins with repeated measures of BMI. I want to determine whether intake of a nutrient is associated with BMI trajectories. I have been using GLS in the ...
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Select autocorrelated events [closed]

I have $N$ timeseries each of length $L$ with $k$ features describing the events that have side $ s \in \{-1, 1\}$. I want to build a model that would select events based on their features i.e. $f : \...
Тимофей Черников's user avatar
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Autocorrelation of the lognormal Black-Scholes process

The Black-Scholes model with constant volatility $\sigma$ and interest rate $r$ is defined as $$ dS_t/S_t=rdt+\sigma dW_t $$ I derived the autocorrelation of the spot process $S_t$ for future times $0&...
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In repeated measures, how to distinguish regression to the mean from a negative lagged effect?

I have repeated measures for a quantitative variable "cry" for N = 52 participants (how much you cry at a given time), there are 30 repeated measures. The values range from 0 (not at all) to ...
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Does autocorrelation in errors always cause problems?

I am preparing a lecture slide on effect of autocorrelation of errors on t-statistic, and I am using a simulation exercise to illustrate the point. However, I am obtaining results that are clashing ...
CrisisStudent's user avatar
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Estimation of autocorrelation from unevenly sampled time series

Consider $n$ distinct time series $X^{(1)}, \ldots, X^{(n)}$, indexed by time (time ranging from 0 to 1), such that: each time series $X^{(i)}$ has a different number of observations, the time ...
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Transformed Ornstein Uhlenbeck process

Say I have 𝑋 that follows an Ornstein-Uhlenbeck process: $𝑑𝑋_𝑡=𝜙X_t𝑑𝑡+𝜎𝑑𝑊_𝑡$ Let $𝑌_𝑡=exp(𝑋_𝑡)$. How can I calculate the autocorrelation function of $Y_t$?
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Violation of i.i.d assumption in time series modeling

In time series forecasting,let's say you have $x_1, x_2, x_3, \cdots, x_t$ and the goal is to predict the the value of $x_{t+1}$ given values at previous times $1,\cdots,t$. Let's assume that the ...
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How to split and sample "Panel Data" when training a Logistic Regression to predict future outcomes

Introduction I have panel data where customer behavior is observed over time. For each customer at a given reference date, I have a lookback window of 12 months for generating features, and a look ...
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Time series regression on mixed frequency overlapping data

I have an hourly univariate time series. I am trying to see if the next hour, day, week etc changes are forecastable from the past changes. The ACF and PACF of the data both look similar and show some ...
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Residual autocorrelation in ARMA-GARCH model

I have used the auto.arima function on my data set, which is the Ethereum-USD exchange rate, and I end up with an ARMA(2,2) model based on the AIC. I have estimated ...
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Understanding Contradictory Autocorrelation Findings in Residual Analysis

Question I came across an answer regarding how to evaluate the autocorrelation of residuals. However, when I apply two different approaches, the Durbin-Watson test (Fig. 1) and creating time-lagged ...
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Covariance matrix of sliding windows of a time series

I have a non-stationary time series $\{X_t\}$ (it is a stock price) and from this set I collect sliding windows of length 400 timesteps $\{Y^i_\tau\}$ where $i$ labels the window and $\tau \in [1,400]$...
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Why is a coefficient in front of $Y_{t-1}$ in a random walk (equal to 1) not an autocorrelation coefficient? [duplicate]

As it is said everywhere autocorrelation measures the correlation between a time series variable and its lagged values at different time intervals. Then why can't we say that coefficient in front of $...
Nika's user avatar
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Which way to correct for autocorrelation in GAM in timeseries (corARMA/corAR1/corCAR1)?

I was wondering if there are any noteworthy differences in how to correct for $\text{AR}=1$ in a GAM, where time is continuous considering the three different methods here (the data has been collected ...
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Autocorrelation and ARMA model

Consider the market model for security $i$ $$ R_{i,t}=α_i+β_i R_{m,t}+e_i $$ I'm estimating the parameters of this model (alpha and beta) using OLS. However, the Breusch-Godfrey test indicates the ...
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Degrees of freedom for biased sample autocorrelation function

I want to find the expression for the a biased estimate of the autocorrelation function for a time series $X$, and am doing this from the biased estimated autocovariance function for lag $k$, divided ...
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Why does differencing White Noise induce autocorrelation of $-0.5$?

I am curious about the following problem. Let's have a variable given by white noise, $$y_t \sim \operatorname{NID}(0,1).$$ Let's say we difference it, $$\Delta y_t = y_t - y_{t-1}.$$ And now, if we ...
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What is the formula to compute the height of significance line on autocorrelation plot?

Autocorrelation of a time series can be plotted in R with use of acf function. For example: acf(ldeaths) # built-in series I ...
Brzoskwinia's user avatar
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How to implement Newey-West standard errors in R?

Im trying to implement newey-west standard errors to correct for issues i had with autocorrelation doing a regression with OLS. But these robust errors only make my results less significant. I have ...
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Regressors Became Statistically Insignificant Upon Correcting for Autocorrelation

I am using Stata and used the regress command and received $p$ values that indicate the regressor is statistically significant. However, after plotting the residuals, I noticed there was clearly an ...
William H's user avatar
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r mixed model unstructured and ar1 covariance matrices

My goal is to specify two different covariance matrices for two different random intercepts. Briefly, this is my dataset. Outcome is continuous (school test scores) 13 Schools in my study. Random ...
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Standard deviation of an autocorrelated time series

Given a time series of log returns $R_t$ with significant autocorrelation up to $k$ lags, what is the formula for the standard deviation of $R_t$ that accounts for this autocorrelation? I've seen the ...
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Why does the serial.test function from the vars package in R yield contradictory results for type='BG', 'ES', and 'PT.asymptotic'?

I fitted a VAR model, individually all the residuals do not have autocorrelation, but if I use the serial.test I get different results: Type 'ES' Edgerton and Shukur (1999) Test p.value=0.99 Type 'BG'...
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Correlation structure in model residuals

I ran some analysis, and I would feel much more confident with the feedback of the community. I do not provide a MWE (but I would be glad to do so if you feel the need) as I consider this query more ...
Keyvan's user avatar
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Long-run variance for an AR(1), with simulation

For a stationary (and absolutely summable), mean-zero (just to make this easier) time series $y_t$, with $\gamma_j=\mathrm{Cov}(y_t,y_{t-j})$, the long-run variance $$\mathcal{J}=\sum_{j=-\infty}^{\...
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Autocorrelation of discontinuous time series data [closed]

I am attempting to perform an autocorrelation study using python on a discontinuous time series dataset. To share a bit about how my data looks like, it is a single column of values, which spans over ...
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Linear regression with smoothed time-series as independent and dependent variables

I'm pretty sure I'm misunderstanding something quite obvious here but I'm rather confused. I have multiple time-series that have been smoothed with a gaussian kernel. My goal is to regress the time-...
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Reference for autocorrelation formula for vectors

This post on Stack Overflow says that the autocorrelation, or self correlation, of vectors is defined as $$C(t, \{v\}_n) = \frac {1}{n-t}\sum_{i=0}^{n-1-t}\vec v_i\cdot\vec v_{i+t}$$ What is the ...
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Using two-sample K-S test for the same time-series data

I have time-series data which is a recording of neural activity in a neuron before and after some stimuli (I know the specific time when the stimuli was introduced). I'm considering using the two-...
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How can I determine if a system is equilibrated?

Cross-posted in SCSE and MMSE I am experimenting with a new MCMC protocol and new research. In the context of Monte Carlo simulation, a "state of equilibrium" refers to a condition where the ...
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How can I compute the longest relaxation time?

Cross-posted at MMSE and at SciComp. In the case of Monte Carlo simulations: Autocorrelation Time ($\tau_{\text{int}}$): A measure of how many steps are needed for the correlations in the chain to ...
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Is this the correct computation of autocorrelation for lag=1? [duplicate]

I want to compute the autocorrelation for the series {1,2,3,4,5} at lag k=1. I step through the calculation in tabular format. ...
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2 votes
2 answers
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Incorporating ARIMA errors in a linear regression model

I am working with economic data and trying to create a linear regression model for forecasting purposes. The dependent variable data is in terms of percentage change and I've differenced the ...
Amy K's user avatar
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7 votes
1 answer
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Checking for temporal autocorrelation in experience sampling data - how to interpret the variogram?

I have day-level data from about 100 participants from 11 days (EDIT. a subset of participants responded for 12 days, which is why there's a distance of 11 in the variogram table). I'm interested in ...
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Estimating the expected autocorrelation x time away given information about how it weakens over time

Let's say I have repeated measurements of some (approximately normally distributed) variable spaced 7 days apart. Is there some way to use the information in these week-to-week correlations to ...
Vilgot Huhn's user avatar
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Autocovariance function of autoregressive process, generalized to any order

I have calculated the autocovariance function in the AR(1) case, which was quite easy, but I need the autocovariance function for higher order AR(p), assuming it is still stationary. I have been ...
Dylan Way's user avatar
3 votes
2 answers
171 views

What am I missing in the vector case?

I obtained two sets of data from a Monte Carlo simulation of polymer movement. One is a list of $r^2_{end-to-end}$, ...
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Covariance matrix of autoregressive process, any order

Consider the model $$x_i=\rho_1x_{i-1}+\rho_2x_{i-2}+\dots+\rho_px_{i-p}+\omega_i,\:\mathbf{\omega}\sim N(\vec0,\mathbf{I}\sigma^2)$$ In the case of order 1 autocorrelation (i.e. where $\rho_2$ and up ...
Dylan Way's user avatar
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Selecting the Lag and then Aggregating the Data to Control Chart Autocorrelated Extrusion Data?

I have wall thickness data from an extruded product. I understand that for use in a control chart (XmR) that data from extruded products will be autocorrelated. My data was sampled every 5 seconds ...
Chris's user avatar
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1 answer
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Test serial correlation for panel data

I have a set of panel data (including variables X1, X2, X3. and N=193; T=22) these variables are used as independent variables in the model. I want to check the autocorrelation of each of these ...
Huy Lê Thanh's user avatar
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Dirichlet/multinomial dirichlet model with autocorrelation

I need to estimate an inferential statistical model of a variable that is a set of 8 proportions that sum to 1. The data repeat for 25 years and the series is an AR1 process. Is there a statistical ...
Heather Ba's user avatar
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Do you change the mean / standard deviation when calculating the unbiased normalised autocorrelation function?

I am trying to calculate the unbiased normalised autocorrelation function. I think this field is a little complicated as different sources appear to use different nomenclature to describe the same ...
Steven Thomas's user avatar
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How do I appropriately code a gamm() model with an inverse.gaussian family and autocorrelation structure?

I am incredibly new to generalized additive modeling, so I apologize in advance for any and all naiveté. But I believe GAMMs are the appropriate methodology for my data. I am working with fish ...
babygammer's user avatar
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What does this autocorrelation plot mean? [duplicate]

Is there any definitive meaning to a sinusoidal (above and below zero line) autocorrelation v lag plot? What does it tell us, if anything, about the realization it came from?
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Cochrane-Orcutt procedure with higher-order differencing

I have a set of monthly time series data, and I would like to fit regression models with exogenous variables (price) to a response (sales volume). The errors are surely autocorrelated, and I need a ...
Arthur's user avatar
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Issue with coefficient estimate in linear trend regression model with autocorrelation of residuals

The question is simple, generally the coefficient estimate is not affected by autocorrelation of residuals when the independent and dependent variable are distinct. I am not sure about the clear ...
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