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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Why are the autocorrelation computations without FFT and with FFT giving different results?
Related: Reference for autocorrelation formula for vectors
The original formula for the computation of the autocorrelation of vectors is:
$$C(t, \{v\}_n) = \frac {1}{n-t}\sum_{i=0}^{n-1-t}\vec v_i\...
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On assumptions of local projection method
It is well known that Jorda(2005) proposed the following model called local projection:
$$y_{t+h} - y_{t-1} = \beta_h shock_{t} + \gamma_h ctr_{t-1} + \epsilon_{t,h}, h = 0,1,2,\dots,H.$$
I am trying ...
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Why does accounting for autocorrelated residuals barely help parameter estimation in distributed lag models
This problem has been plaguing me for a long time. Basically, I have a distributed lag model $$y_t=\sum_{i=0}^{p} \beta_i x_{t-i} + u_t.$$
The regression problem is a bit misspecified, so I end up ...
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Tradeoff between autocorrelation and memory in a GLMM
I am working with a large dataframe in R. It is a BACI design (Before-After-Control-Impact). I am interested in seeing if the interaction between Treatment (0 = control, 1 = impact) and Period (Before,...
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Is the OECD BCI Dataset fit for use with Linear Regression?
I am wondering if the OECD Business Confidence Index can be utilised by a linear regression model for time-series data.
I have had a look at the ‘basis of prep, for the data and I am rather confused (...
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How should I go about completely decorrelating a digital signal?
So I'm working on real time signal compression, and I need to come up with the best convolution to minimize the entropy of incoming data (which I will then compress), which I understand is achieved by ...
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R - Why is bgtest showing no autocorrelation when order is set to a higher number, but shows autocorrelation at order = 1
Upon reading, I saw that bgtest (Breusch-Godfrey test, from lmtest pkg) can diagnose autocorrelation of higher orders than just 1, which is the maximum order the dwtest (Durbin-Watson test, from ...
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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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How Does Serial Correlation Cause OLS to remain unbiased (even in cross -sectional data)
In order for the coefficient estimators to remain unbiased in OLS, the conditional expectation of errors given the regressors needs to be zero, $E(u_i |x_i )=0$.
However, if we have serial correlation ...
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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 ...
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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 $...
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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 ...
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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 ...
J_caesar
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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 ...
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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 ...
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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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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 ...
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