A Note on the Asymptotic Normality Theory of the Least Squares Estimates in Multivariate HAR-RV Models

Won-Tak Hong, Jiwon Lee and Eunju Hwang
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Won-Tak Hong: College of International Studies, KyungHee University, Yongin 446-701, Korea
Jiwon Lee: Department of Applied Statistics, Gachon University, Seongnam 13120, Korea
Eunju Hwang: Department of Applied Statistics, Gachon University, Seongnam 13120, Korea

Mathematics, 2020, vol. 8, issue 11, 1-18

Abstract: In this work, multivariate heterogeneous autoregressive-realized volatility (HAR-RV) models are discussed with their least squares estimations. We consider multivariate HAR models of order p with q multiple assets to explore the relationships between two or more assets’ volatility. The strictly stationary solution of the HAR( p , q ) model is investigated as well as the asymptotic normality theories of the least squares estimates are established in the cases of i.i.d. and correlated errors. In addition, an exponentially weighted multivariate HAR model with a common decay rate on the coefficients is discussed together with the common rate estimation. A Monte Carlo simulation is conducted to validate the estimations: sample mean and standard error of the estimates as well as empirical coverage and average length of confidence intervals are calculated. Lastly, real data of volatility of Gold spot price and S&P index are applied to the model and it is shown that the bivariate HAR model fitted by selected optimal lags and estimated coefficients is well matched with the volatility of the financial data.

Keywords: multivariate HAR models; least squares estimation; asymptotic normality; exponentially weighted HAR models (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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