Questions tagged [heteroscedasticity]

Non-constant variance along some continuum in a random process.

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Is there a decisive way of accepting/rejecting homogeneity and normality tests?

While learning about regression, I was told as a prerequisite for significance testing you must test for normality and homogeneity. I can do this by plotting Q-Q plots and residuals to fitted values, ...
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Heteroscedasticity across one dimension in a panel setting

I understand that in a regression setting, heteroscedasticity is present if the vector of residuals of a model has non-constant finite variance. Say you have a (balanced) panel across $i \in I$ and $t ...
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Can you us logged returns for both dependent and independent variables in GARCH? [closed]

I'm doing exchange rate returns forecasting using GARCH-M model. My mean equation uses commodity prices as independent variables. So I see literature talking about using logged returns, but don't ...
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Breusch Pagan Test for individual factors

So if I have a multiple regression model and I want to test, which factors are related to the residuals using the Breusch Pagan test. If I use the bptest() function in R by regressing the squared ...
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Question about heteroscedascity and point estimates

Let's say I am running a regression: $y_{j}=\beta x_{j} + \eta_j$ and $var(y_i|x_i)=var(\eta_i|x_i)=f(x_i)$, say the variance is increasing in x. assume $\eta$ is fully independent of x, so ...
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Why is variance a fixed constant when modelling Linear Regression through MLE?

I was following a derivation of Linear Regression through MLE. Here we model Then we proceed to derive the negative log-likelihood through a series of steps as shown. Finally we maximize the above ...
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Best model for various bad situations

"What type of predictive model would best handle a wide variety of data issues. Extreme heteroscedasticity bi or tri modal distribution’s heavily correlated predictors… Saw this as an Amazon ...
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Are autocorrelation, heteroscedasticity and normality of residuals used in non-linear models?

I have a very simple non-linear model: lm(Y ~ poly(X, degree = 2), data=data) The results I obtained are: My question is, to test the validity of the model, is ...
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Do I need to check for Autocorrelation, Heteroskedasticity and Normality when building a model with data that are not time series? [duplicate]

I want to build a simple regression model with non-time series such as Client ID Number. when testing the validity of this model, do I need to check for autocorrelation, Heteroskedasticity and ...
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How do you check whether heteroscedastic-consistent estimators fix your error variance problem?

I am running an OLS regression, and have non-constant error variance (residuals vs fitted looks like a fan opening up to the right). I have tried a number of power transformation but they seem to make ...
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which test to do first? [duplicate]

I have a dataset that has 4 Columns as x axis. I want to check the data for: Autocorrelation, Multicolinearity, Heteroscedasticity and Normality, In what order should ı perform the tests? And ıf my ...
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How to calculate Newey-West adjusted covariance matrix?

I have a $T \times N$ matrix of asset returns, where $T$ = number of periods, and $N$ = number of assets. Calculating the covariance matrix of this set of returns is simple. How do I calculate the ...
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Mathematical notation of a mixed effect model with different variance structures

I am assessing the relationship between a response variable (Y) and a predictor (X) using repeated measures in 6 individuals (...
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Sampling from a distribution which results in heteroskedasticity

I have a pretty basic model whereby using a monte carlo approach I am seeking to recreate the monthly stock market returns over the last 30 years. Using the actual monthly returns of an index, I have ...
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Dealing with heteroskedasticity in negative binomial GLM

I'm analyzing a harvest dataset and I'm trying to figure out which parameters influence hunting success. My data is a daily number of hunted birds and I have multiple covariates, effort (number of ...
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F-test for homogeneity with infinite degrees of freedom

I'm trying to replicate a previous analysis that is lacking in documentation. I am comparing estimated values between weeks to evaluate whether I should combine groups for analysis. The previous ...
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Question about ols standard errors if using age adjusted rates as a dependent variable

if I am running an age adjusted rate, say fertility rate, as a dependent variable in a regression- so say for county c: $y_{c}=\beta X_{c} + \eta_c$ where $y_c$ is the age adjusted rate defined as in ...
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Interpretation of scatter plot - vertical line patter spotted

can I please get quick help on this scatter plot of standardised residuals against predicted values. Does this mean this violated normality, linearity and homogeneity? How should I interpret that ...
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Question about OLS and BLUE in the presence of hetereoscadasticity and robust standard errors

My understanding that if errors are non-spherical, OLS is no longer the minimum variance linear unbiased estimator (assume the error terms are fully independent of all covariaties- so unbiasedness ...
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Metropolis-Hastings for linear regression, prior on sigma?

For the sake of curiosity, I'm trying to build a Metropolis-Hastings sampler for the purposes of Bayesian linear regression. Below, you'll note my script and more specifically, in-line comments that ...
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1) Testing for homogeneity within a group and 2) testing if factors affect outcome

I am a research intern at a plant breeding company and do not have much SPSS experience and would like some advice considering this question/research. The added image visualizes steps 1 to 4; see ...
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Clusters in fitted vs residual plot; indication of some underlying and unaccounted for variable?

I'm analyzing some data on frog calls (model output in pic 2), and I'm running into trouble due to my linear mixed models not meeting the assumption of homoscedasticity. That's something I've run into ...
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1answer
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Correct regression model for independent variable limited 0-100

So I'm having some questions about a regression model I'm trying to fit The dependent variable is a continuous interval scaled index reaching from 0 to 100. It's severely left-skewed and most ...
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Parameter constraint using gnls() function of nlme package

I'm having a problem to fit model with parameter constraint. I noticed that gnls function inside nlme package doesn't have ...
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1answer
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How to show that an m.d.s is not independent?

I have to prove that this Martingale Difference: $x_t = u_t u_{t-1}$ where $u_t \sim^{iid} (0, \sigma^2)$ is not serially independent, but am failing to do such thing. I also have to prove that it's ...
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How to decide between different robust standard errors?

Specifying my model I ran into some very mild heteroscedasticity problems. Given its superior small-sample properties (my dataset contains 79 observations) I used the HC3 specification of the White ...
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Does HC3 correction for unequal variances work in mixed ANOVA?

Since equal variances are necessary for any ANOVA that contains between-subject factors – regardless of whether it also contains within-subject factors – all such cases need correction (or alternative,...
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Statsmodels heteroskedasticity test: consider weight of data next to difference in variance

For a current project, I have generated a number of data points that show a clear triangular pattern: When trying to quantify this pattern through a Statsmodels Breusch-Pagan test, the data however ...
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How to forecast $Y/std(Y)$ using a linear model?

How do I forecast $Y/std(Y)$ using a linear model? I'm currently forecasting only $Y$, and the model is producing results where the larger predictions corresponding to higher variance $Y$. For example,...
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In a multilinear regression, does the usage of White standard errors always correct for heteroscedasticity?

I've calculated a multilinear regression. When testing the assumptions of linear regression, I've come to understand that my model violates the assumption of homoscedasticity (as shown with a Breusch-...
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1answer
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How can i test the heteroscedasticity of time series?

This is my first post here and it's a pleasure to join this community. I'm a finance research student and actually i'd a problem on testing the heteroscedasticity caracteristics of my time series ...
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How should I transform this time series such that the magnitude of each value can be compared without the effect of the decreasing variance?

this is my first post and it's nice to join this community. I'm not exactly an expert at statistics, but I really enjoy it. The following problem has become somewhat of an enigma for me. I have this ...
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Knowing when the variance in a time series is changing

A basic question, but one I have not found. It is said that if your variance is changing over time you should log it before running ARIMA. This is a form of non-stationarity but I have not seen ...
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The impact of geometric and arithemtic mean on heteroscedasticity

assuming I have a time series and want to do a regression on it. I see that the residuals are heteroscedastic, e.g. that the variance is proportional to the mean. A remedy for this is/can be the log-...
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How to find out conditional probability distribution of dependent variable given the independent variable in quantile regression?

Suppose I'm given a problem of estimating future values of a particular entity, treating it as a linear regression problem, assumptions of linear regression model like heteroscedasticity are violated. ...
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How to correctly deal with outliers that induce heteroscedasticity?

So I´ve stumbeled across the the question of how to correctly deal with outliers and found an array of recommendations and possible "solutions". However I did not feel really enlightened ...
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Does there exist an analytical solution to the log-likelihood minimisation for a Gaussian model with linear variance?

I'm trying to model some data using the following distribution: \begin{align} r &\sim \mathcal{N}(\mu, \sigma^2) \nonumber\\ \mu &= m_0 + m_1 d \nonumber\\ \sigma^2 &= s_0+s_1 d\nonumber\\ ...
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How to add weights in KNN and Decision Tree Regression

I am using a data that has multicollinearity and heteroscedasticity present in it. I am using KNeighbours Regression and Decision Tree Regression in sklearn to model the data and make predictions. I ...
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consequences of using SARIMA on heteroscedastic data

If I were to run SARIMA on data that was heteroskedastic how would it affect my model? I know in OLS the heteroskedascity only changes my standard errors and not the coefficients themselves, is that ...
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Autocorrelation test robust to heteroskedasticity

I'm testing the random walk hypothesises 1 and 3. I'm done with the first hypothesis but am struggling with the test distribution of the third one. I'm using the autocorrelationstest. For the first ...
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ANOVA curve representation

I am researching the embodied cognitive intent exhibited by archeological assemblage, e.g., in ancient glass. I work out homogeneity by ANOVA so as to suggest a Levene's value. For both the real ...
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Calculation of Olea and Pflueger's (2013) Effective F-statistic

I am trying to understand the calculation of Olea and Pflueger's (2013) test for weak instruments when the errors are not conditionally homoskedastic and serially uncorrelated, which is calculated as: ...
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Checking the constant variance assumption for residuals vs fitted plots: What about for the same fitted values?

For a residuals vs fitted plot, we use the fitted values $\hat{Y} = \beta_0 + \beta_1 + \cdots + \beta_p x_p$ on the horizontal axis and the residuals on the vertical axis, and then compare the ...
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Heteroskedasticity leads to inconsistent estimate in log-linear model

My question concerns the following paper. Silva, J. M., & Tenreyro, S. (2006). The Log of Gravity. Review of Economics and Statistics, 88(4), 641-658. doi:10.1162/rest.88.4.641 To summarize, ...
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What does it mean if magnitude of the variance of each measurement is allowed to be a function of its predicted value?

To better understand Logistic Regression and why it is called regression still, I was reading about Generalized Linear Models on Wikipedia, and I came across the below statement: "The GLM ...
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How to model variance of a heteroskedastic dataset

I have a dataset (scatter plot shown below) where x-axis corresponds to observed value and y-axis being the true value (yeah, sort of flipped from the convention where y is the observed value). I am ...
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MANOVA for equal sample sizes, non-independent samples, and heteroskedasticity for time series data

I am looking for a MANOVA-like procedure testing for equal mean vectors for populations that allows for dependent samples (probably because the data are time series and the vectors are correlated), ...
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Imprecision of coefficient estimates can lead to slightly larger errors?

I'm looking into how to diagnose homoscedasticity. In http://people.duke.edu/~rnau/testing.htm, it states "Because of imprecision in the coefficient estimates, the errors may tend to be slightly ...
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Plotting residuals vs fitted values or vs independent variables?

I've seen posts where residuals were plotted against fitted values $\hat{y}$ and posts where they were plotted against the independent variable (assume simple linear regression for simplicity). When ...
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Alternative to Mixed ANOVA without homogeneity of variances

As is tradition on these posts, I should say I'm relatively new to statistical analysis at this level so if I don't provide enough info off the bat bear with me. So I've conducted an experiment ...

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