Questions tagged [heteroskedasticity]

refers to non-constant variance of errors across different observations

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Showing the unbiased estimator of variance for GLS estimator

I have the following regression $$y = X\beta +u$$ where $y$ and $u$ are $(n\times 1)$ and $X$ is a fixed $(n \times k)$ matrix with full column rank and $\beta$ is an unknown $(k\times 1)$ vector of ...
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1 vote
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WLS or Feasible GLS?

For a question like this, would I use WLS or Feasible GLS? I am leaning towards WLS but my lecture slides tell me GLS is used when there is more than one variable that drives the residual variance.
1 vote
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Wald Statistic with heteroskedasticity on asymptotic inference vs exact inference

I was working on the following proof but I got stuck. I'm trying to show that the next equality holds: $$(X'X)^{-1}X'\mathbb{E}_n[\varepsilon\varepsilon']X(X'X)^{-1} = \mathbb{E}_n[XX']^{-1}\mathbb{E}...
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1 answer
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Annual Data and Heteroscedasticity (Engle's ARCH test)

GARCH models are often applied to financial time series (daily, weekly or monthly stock returns). What about lower frequency such as quarterly and annual time series? This could include macroeconomic ...
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2 answers
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Arch Model and $\sigma$

In my problem set about ARCH models I'm given that $\epsilon^2_{t}=\alpha\epsilon^2_{t-1}+v_{t}$ But then I'm asked to calculate $E(\sigma^2_{t+n}|I_{t-1})$. So is the same to calculate $E(\epsilon^2_{...
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Is this weighted least squares or just weighting the dependent variable

I am a little confused as to what the following line means. Do the authors mean they run a weighted least squares using the sample size as weights, or just weight the dependent variable using the ...
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1 answer
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Understanding General Least Squares

From what I understand, we have our OLS estimator in matrix form which is, $$\beta_{OLS} = (X'X)^{-1}X'Y$$ What we want to do is transform this, as the assumption that we have constant variance is ...
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3 answers
86 views

Heteroskedasticity assumption in fGLS into linear form?

I am following Chapter 8 ("Heteroskedasticity" p. 259) in the 6th edition of Woolridge Introductory Econometrics: A Modern Approach and I don't understand one piece of the transformation of our model. ...
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313 views

Asymptotic variance under heteroskedasticity

I want to find an expression for the asymptotic variance of the OLS estimator given that the errors are heteroskedastic. I have understood the derivation using CLT for the homoskedastic case. I.e., $...
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4 votes
1 answer
225 views

Heteroscedasticity and weighted least square estimator

"In presence of heteroscedasticity, OLS estimators are unbiased but inefficient" Showing the unbiased part is relatively easy. Some authors have explained the inefficiency with the help of new ...
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1 vote
1 answer
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possible Heteroskedasticity?

Based on the graph, would you say that there is some sort of heteroscedasticity in the data? Y-axis is residual squared and X-axis is predicted values of Y
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Testing for heteroskedasticity in panel data vs time series?

I watched this video on how to check for heteroskedasticity using Stata, and it helped me a lot. But the data example in the video was time series data. He used the Bruesh-Pagan test. ...
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