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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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Which statistical analysis should I use (on R) on a multivariate GAMM accounting for spatial autocorrelation?

Part 1 : Including categorical variable in my formula I have 3 dependent variables (DVs ; Y1, Y2, Y3) which are continuous and 2 independent variables (IVs) with one which is continuous (X1) and the ...
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What do my first difference ACF/PACF show me?

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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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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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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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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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 ...
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ACF plot shaded blue region

Please see ACF plot attached (Python). I would like to understand why the shaded region of my plot takes a curved shape? My understanding so far is that the confidence band changes because the ...
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The consequences of ignoring autocorrelation of errors for the LASSO estimator?

In ordinary linear regression, Y = X$\beta$ + $\epsilon$, if the error is autocorrelated, then the assumptions under the Gauss-Markov theorem are violated. For example, autocorrelation violates the ...
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36 views

Incorrect Approach to Multiple Time Series Forecasting

I am working on a problem where I want to forecast multiple time series. We have time series data in the following format: ...
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GARCH, EGARC, GJR-GARCH EViews

I'm using Eviews to model and forecast volatilities for 6 different stock markets( it's for my dissertation). I found serial correlation in almost every log-return and even after running the GARCH ...
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Estimate the asymptotic efficiency of a Markov chain sampling by the method of batching

In the paper Efficient Metropolis Jumping Rules, the author is writing that he used "the method of batching" for the estimation of $\operatorname{eff}_{\overline\theta_i}$ in Table 1 (on page 605). ...
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Q: Implications of autocorrelation in a Dickey-Fuller unit root test

I am conducting a Dickey-Fuller unit root test on the FEDFUNDS series from the FRED database. My estimation period is quarterly from 1955(1) to 2007(4) (taking the average of the monthly rates within ...
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auto-correlation and OLS regression

I was trying to find the OLS estimator for the model: $Y$ = $\beta_0$ + $\beta_1X_{1t}$ + $\beta_2X_{2t}$ +.......+ $\beta_5X_{5t}$ + $e$ t = 1,2,3 ......, 50 time ordered observations X is a full ...
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Spatial auto-correlation function of $\sin^2(2\theta)$ in terms of that of $\theta$

Let $\theta$ be an isotropic random field which has a unifrom pdf $U[0,2\pi]$ and whose auto-correlation function is $R_{\theta \theta}(|y-x|) = \mathbb{E}[\theta(x)\theta(y)]$ wherein x and y are ...
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Exponential autocorrelation during generation of 2d Gaussian random field

Here is the problem...If I generate exponentially correlated row ${x}_{0,0}, {x}_{1,0} ... {x}_{n,0}$ and starting from ${x}_{0,0}$ there will be a correlated column ${x}_{0,0}, {x}_{0,1} ... {x}_{0,n}...
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How to use correlation function? [closed]

If I have a normal distribution and some autocorrelation function $\rho(\tau) = Exp[-\tau/\xi]$. Where $\xi$ is a correlation length, $\tau$ is a lag. How to use it? Does it mean $Correlation({\tau}_{...
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Number of lags in Ljung-Box test for feature extraction

I'd like to cluster time series based on static features, one of which is the Ljung-Box autocorrelation. After reading this question on "How many lags to use in the Ljung-Box test of a time series", I'...
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Why is the ACF diagram showing seasonal patterns when they should have been removed by `decompose`?

I'm reading the book Introductory Time Series with R where the following code is given: ...
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Autocorrelated independent variable (how to treat)

I have some response variable $Y$ that I am trying to model with OLS. There is a single independent variable $X_{t,N}=Y_t-Y_{t-N}$ for some $N$. However, when I do such a simple regression, I obtain ...
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54 views

MCMC autocorrelation

I have a MCMC simulation that tries to fit a line to a linear set of data. The auto-correlation is very high for the slope parameter (~0.9), and low (~0.05) for the bias What does a high auto-...
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How to account for temporal autocorrelation in logistic regression with longitudinal data?

I am attempting to perform a logistic regression on longitudinal data (game camera footage of nesting birds, with a photo taken every 5 minutes for a period of 10-28 days, depending on whether the ...
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Estimating population concentrations in spatially autocorrelated data

I'm stuck on which statistic to use with a spatial data set to resolve population concentrations in a large area, when I have only sampled a small area relative to that large area. Here's an example ...
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How to calculate the coefficient of the model MA (1), with negative discriminant

In the calculation of the coefficient of the model MA(1) the following formula is used. For example, if the first value of acf=0.1923, the discriminant is D=B^2-4*A*C. D=0.85208 The solution has two ...
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How can we numerically compute the autocorrelation of a sample from a Markov chain generated by the Metropolis-Hastings algorithm?

Let $(X_n)_{n\in\mathbb N_0}$ denote a $\mathbb R^d$-valued Markov chain generated by the Metropolis-Hastings algorithm. Suppose I've run the algorithm on a computer and obtained a sample $x_0,\ldots,...
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incorporating temporal autocorrelation into GLMM

I am examining the relationship between presence at a site over time, and I am interested in determining if there is a decline in presence as an individual gets closer to their final departure. Due ...
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How to account for temporal autocorrelation in mixed effects logistic regression?

Apologies if this has been asked before-I've looked around but haven't found any questions regarding my exact situation. I am conducting a study aimed at determining the climate sensitivity of a bird ...
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How can I map a Gaussian vector according to an equation that has a spatial autocorrelation function?

I have the following function: $E(x,z)=30-0.5z+12.5\frac{e^{Y(x,z)}-e^{0.5}}{\sqrt{e^2-e}}$ I want to run some Monte Carlo simulations and at each simulation I have to generate values for $E$ at ...
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Autocorrelation in residuals

Hi guys, thanks for your time! Problem description: I am working with dynamic factors. I have 4 panels of 24 series (hourly electricity prices) and I reduce them to 1 dynamic factor each that I then ...
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Best way to measure reliability of auto-correlated data

I'm trying to compare different ambulatory devices for measuring heart rate against a gold standard in-lab assessment. What is the best way to determine whether a device is worth using. I can use ...
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22 views

Confidence interval of mean for time series

I have data from a humidity sensor and would like to estimate the confidence interval of its mean value. However, since the time stamps are "too close together" the data-points are correlated. ...
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temporal autocorrelation machine learning algorithms

I am trying find out the relationships of stream integrity against Land uses. I have 4-years of stream integrity data (1998-1999, 2004, 2009, 2014) and corresponding land use data of 1995, 2002, 2007, ...
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How to define Autocorrelated Copula?

I want to make a copula between two auto correlated timeseries.Since it would be better for the timeseries not to be auto correlated, was thinking about making ARIMA (Autoregressive Integrated Moving ...
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Stationarity test for autocorrelation

can we use unit root test of residual to detect autocorrelation in a time series model? Are stationarity of the residual means there is no autocorrelation?
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How to ensure independence of calibration and validation data a spatial model considering spatial autocorrelation?

I determined the vegetation type (4 types all in all) at 120 points (stratified random sampling) in my study area (650ha). I want to use the points to train a statistic model (eg. random forest) based ...
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Are Poisson Regressions with Serial Correlation Biased or Inconsistent? (No Fixed Effects)

Let's say I've got panel data where a count outcome $y$ and continuous independent variable $x$ observed each time period $t=(1,2,...T)$ for each individual $i$. I am interested in how $x_{it}$ ...
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Am I doing the correct data transformation for Granger causality tests

I have seven sets of time series, below is my process flow, am I doing the correct thing here? especially step 4. Raw data transform and test stationary with unit root test (ADF), with level, first ...
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Should I use weekly or daily returns for modelling FX returns?

I am currently modelling Foreingn Exchange returns using a GARCH model. I am simulating returns 1-year forward. Would it be better to use weekly or daily data on Foreign Exchange returns? Weekly data ...