Kernel-based Volatility Generalised Least Squares

Ilias Chronopoulos; George Kapetanios; Katerina Petrova

doi:10.1016/j.ecosta.2019.11.001

Kernel-based Volatility Generalised Least Squares

Ilias Chronopoulos, George Kapetanios, Katerina Petrova

Banking & Finance

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

The problem of inference in a standard linear regression model with heteroskedastic errors is investigated. A GLS estimator which is based on a nonparametric kernel estimator is proposed for the volatility process. It is shown that the resulting feasible GLS estimator is T-consistent for a wide range of deterministic and stochastic processes for the time-varying volatility. Moreover, the kernel-GLS estimator is asymptotically more efficient than OLS and hence inference based on its asymptotic distribution is sharper. A Monte Carlo exercise is designed to study the finite sample properties of the proposed estimator and it is shown that tests based on it are correctly-sized for a variety of DGPs. As expected, it is found that in some cases, testing based on OLS is invalid. Crucially, even in cases when tests based on OLS or OLS with heteroskedasticity-consistent (HC) standard errors are correctly-sized, it is found that inference based on the proposed GLS estimator is more powerful even for relatively small sample sizes.

Original language	English
Journal	Econometrics and Statistics
DOIs	https://doi.org/10.1016/j.ecosta.2019.11.001
Publication status	Published - 1 Dec 2019

Keywords

Heteroskedasticity
Stochastic volatility
Weighted least squares

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10.1016/j.ecosta.2019.11.001

https://linkinghub.elsevier.com/retrieve/pii/S2452306219300644

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title = "Kernel-based Volatility Generalised Least Squares",

abstract = "The problem of inference in a standard linear regression model with heteroskedastic errors is investigated. A GLS estimator which is based on a nonparametric kernel estimator is proposed for the volatility process. It is shown that the resulting feasible GLS estimator is T-consistent for a wide range of deterministic and stochastic processes for the time-varying volatility. Moreover, the kernel-GLS estimator is asymptotically more efficient than OLS and hence inference based on its asymptotic distribution is sharper. A Monte Carlo exercise is designed to study the finite sample properties of the proposed estimator and it is shown that tests based on it are correctly-sized for a variety of DGPs. As expected, it is found that in some cases, testing based on OLS is invalid. Crucially, even in cases when tests based on OLS or OLS with heteroskedasticity-consistent (HC) standard errors are correctly-sized, it is found that inference based on the proposed GLS estimator is more powerful even for relatively small sample sizes.",

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T1 - Kernel-based Volatility Generalised Least Squares

AU - Chronopoulos, Ilias

AU - Kapetanios, George

AU - Petrova, Katerina

PY - 2019/12/1

Y1 - 2019/12/1

N2 - The problem of inference in a standard linear regression model with heteroskedastic errors is investigated. A GLS estimator which is based on a nonparametric kernel estimator is proposed for the volatility process. It is shown that the resulting feasible GLS estimator is T-consistent for a wide range of deterministic and stochastic processes for the time-varying volatility. Moreover, the kernel-GLS estimator is asymptotically more efficient than OLS and hence inference based on its asymptotic distribution is sharper. A Monte Carlo exercise is designed to study the finite sample properties of the proposed estimator and it is shown that tests based on it are correctly-sized for a variety of DGPs. As expected, it is found that in some cases, testing based on OLS is invalid. Crucially, even in cases when tests based on OLS or OLS with heteroskedasticity-consistent (HC) standard errors are correctly-sized, it is found that inference based on the proposed GLS estimator is more powerful even for relatively small sample sizes.

AB - The problem of inference in a standard linear regression model with heteroskedastic errors is investigated. A GLS estimator which is based on a nonparametric kernel estimator is proposed for the volatility process. It is shown that the resulting feasible GLS estimator is T-consistent for a wide range of deterministic and stochastic processes for the time-varying volatility. Moreover, the kernel-GLS estimator is asymptotically more efficient than OLS and hence inference based on its asymptotic distribution is sharper. A Monte Carlo exercise is designed to study the finite sample properties of the proposed estimator and it is shown that tests based on it are correctly-sized for a variety of DGPs. As expected, it is found that in some cases, testing based on OLS is invalid. Crucially, even in cases when tests based on OLS or OLS with heteroskedasticity-consistent (HC) standard errors are correctly-sized, it is found that inference based on the proposed GLS estimator is more powerful even for relatively small sample sizes.

KW - Heteroskedasticity

KW - Stochastic volatility

KW - Weighted least squares

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DO - 10.1016/j.ecosta.2019.11.001

M3 - Article

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JO - Econometrics and Statistics

JF - Econometrics and Statistics

ER -

Kernel-based Volatility Generalised Least Squares

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Keywords

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