# 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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### Verifying consistency of heteroscedasticity and autocorrelation robust SEs with a Monte Carlo Experiment

I'm trying to demonstrate the consistency of the default HAC standard errors given in R's sandwhich package via a Monte Carlo experiment. I'm using a linear model ...
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### Unsure if spatial Autocorrelation is present or not

I built a classic linear model with 1000 data points for which I have coordinates. I thus checked for the presence of spatial autocorrelation with a bubble plot of the residuals and with Moran's I ...
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### Generating pseudo-random sample sequence with a given autocorrelation function up to max lag

Assume the variable $X_t$ has a continuous value, sampled over uniform discrete time (time series). I have the full autocorrelation function up to max time lag $l_{max}$. The coefficients may be both ...
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### Suggestions on what model to use (ARMA doesn't seem to be applicable)

My data looks like the following: The ACF and PACF plots look like the following: Although there is some dependence with some lags, I fear taking these too seriously is a form of overfitting. I don'...
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### Time scaling of AR(1) process for modelling financial returns

Process: Consider an AR(1) process with zero mean,* $\lambda_t = \kappa \cdot \lambda_{t-1} + \omega_t$, with $\kappa = 0.9$, $\omega \sim N(0, \sigma_{\omega}^2)$, and $\sigma_{\omega}^2 = 0.00027$. ...
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### PCA and tICA on autocorrelated and/or non-equilibrium data

As you can infer from the title, what if I want to do a PCA or a time-lagged Independent Component Analysis of a process where each of the features I consider are sampled in points that, per each or ...
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### Dealing with autocorrelation in GAMs with proportional response data and categorical predictors

I'm new to GAMs and am trying to figure out how to parameterize and interpret models where the response variable is percent of salmon migrating through a given route and I think there might be ...
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### Interpreting autocorrelation as computed by R acf function in a very simple case [duplicate]

I used to assume that I knew what autocorrelation is and that acf function in R produces what I understand as autocorrelation function, but I must be missing some ...
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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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1 vote
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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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1 vote
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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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