Asymptotic distribution of the cointegrating vector estimator in error correction models with conditional heteroskedasticity

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22 Citations (Scopus)

Abstract

This paper explores the asymptotic distribution of the cointegrating vector estimator in error correction models with conditionally heteroskedastic errors. Asymptotic properties of the maximum likelihood estimator (MLE) of the cointegrating vector, which estimates the cointegrating vector and the multivariate GARCH process jointly, are provided. The MLE of the cointegrating vector follows mixture normal, and its asymptotic distribution depends on the conditional heteroskedasticity and the kurtosis of standardized innovations. The reduced rank regression (RRR) estimator and the regression-based cointegrating vector estimators do not consider conditional heteroskedasticity, and thus the efficiency gain of the MLE emerges as the magnitude of conditional heteroskedasticity increases. The simulation results indicate that the relative power of the t-statistics based on the MLE improves significantly as the GARCH effect increases.

Original languageEnglish
Pages (from-to)68-111
Number of pages44
JournalJournal of Econometrics
Volume137
Issue number1
DOIs
Publication statusPublished - 2007 Mar 1
Externally publishedYes

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Conditional Heteroskedasticity
Error Correction Model
Error correction
Asymptotic distribution
Maximum Likelihood Estimator
Maximum likelihood
Estimator
Reduced Rank Regression
Multivariate GARCH
Normal Mixture
Generalized Autoregressive Conditional Heteroscedasticity
Regression Estimator
Kurtosis
Asymptotic Properties
Innovation
Regression
Conditional heteroskedasticity
Error correction model
Heteroskedasticity
Statistics

Keywords

  • Cointegrating vector
  • Efficiency gain
  • Multivariate GARCH

ASJC Scopus subject areas

  • Economics and Econometrics
  • Finance
  • Statistics and Probability

Cite this

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abstract = "This paper explores the asymptotic distribution of the cointegrating vector estimator in error correction models with conditionally heteroskedastic errors. Asymptotic properties of the maximum likelihood estimator (MLE) of the cointegrating vector, which estimates the cointegrating vector and the multivariate GARCH process jointly, are provided. The MLE of the cointegrating vector follows mixture normal, and its asymptotic distribution depends on the conditional heteroskedasticity and the kurtosis of standardized innovations. The reduced rank regression (RRR) estimator and the regression-based cointegrating vector estimators do not consider conditional heteroskedasticity, and thus the efficiency gain of the MLE emerges as the magnitude of conditional heteroskedasticity increases. The simulation results indicate that the relative power of the t-statistics based on the MLE improves significantly as the GARCH effect increases.",
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