This paper proposes a copula directional dependence by using a bivariate Gaussian copula beta regression with the functional ARCH(1) (fARCH) model to suit high-frequency time series that account for intraday volatilities. With simulated high-frequency data, we show how the copula fARCH directional dependence of intraday volatility can be useful in terms of graphical displays for tick-by-tick price changes in a day. We can perform a test of significance of the copula fARCH directional dependence of intraday volatility by the permutation test, p-value, and bootstrapping confidence interval. To validate our proposed method with real data, we use the Korea Composite Stock Price Index (KOSPI) and the Hyundai-Motor (HD-Motor) company stock data with one minute high-frequency. We show that copula fARCH directional dependence of intraday volatility by B-spline basis function is superior to that by Fourier basis function in terms of the per cent relative efficiency of bias and mean squared error. This research shows that the copula functional ARCH directional dependence of intraday volatility can be an important statistical method to illustrate the directional dependence of intraday volatility in the financial market.
Bibliographical noteFunding Information:
Thanks are due to the referee whose comments led to an improvement in the revised version. The authors would like to thank Professor Ron Reeder and Professor Alexander Aue who provided functional ARCH and GARCH R codes. S.Y. Hwang’s work was supported by a grant from the National Research Foundation of Korea (NRF-2018R1A2B2004157).
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- Directional dependence
- beta regression model
- functional ARCH model