A general threshold GARCH process with volatility asymmetry

We consider the problem of stochastic comparison of general GARCH-like processes for different parameters and different distributions of the innovations. We identify several stochastic orders that are propagated from the innovations to the GARCH process itself, and we discuss their interpretations. We focus on the convex order and show that in the case of symmetric innovations it is also propagated to the cumulated sums of the GARCH process. More generally, we discuss multivariate comparison results related to the multivariate convex and supermodular orders. Finally, we discuss ordering with respect to the parameters in the GARCH(1, 1) case.

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Minimum Hellinger Distance Estimation of a Univariate GARCH Process

Journal of Mathematics Research ◽

10.5539/jmr.v9n3p80 ◽

2017 ◽

Vol 9 (3) ◽

pp. 80

Author(s):

Roger Kadjo ◽

Ouagnina Hili ◽

Aubin N'dri

Keyword(s):

Asymptotic Normality ◽

Almost Sure Convergence ◽

Distance Estimation ◽

Hellinger Distance ◽

Distance Method ◽

Garch Process ◽

Minimum Hellinger Distance ◽

Distance Estimator

In this paper, we determine the Minimum Hellinger Distance estimator of a stationary GARCH process. We construct an estimator of the parameters based on the minimum Hellinger distance method. Under conditions which ensure the $\phi$-mixing of the GARCH process, we establish the almost sure convergence and the asymptotic normality of the estimator.

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The reverse volatility asymmetry in Chinese financial market

Applied Financial Economics ◽

10.1080/09603107.2013.818208 ◽

2014 ◽

Vol 24 (24) ◽

pp. 1555-1575 ◽

Cited By ~ 4

Author(s):

Die Wan ◽

Ke Cheng ◽

Xiaoguang Yang

Keyword(s):

Financial Market ◽

Volatility Asymmetry

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Leverage Effect and Volatility Asymmetry

Current Issues in the Economy and Finance of India - Springer Proceedings in Business and Economics ◽

10.1007/978-3-319-99555-7_9 ◽

2018 ◽

pp. 131-150

Author(s):

Parthajit Kayal ◽

S. Maheswaran

Keyword(s):

Leverage Effect ◽

Volatility Asymmetry

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Regime-Dependent Good and Bad Volatility of Bitcoin

Journal of Risk and Financial Management ◽

10.3390/jrfm13120312 ◽

2020 ◽

Vol 13 (12) ◽

pp. 312

Author(s):

Kislay Kumar Jha ◽

Dirk G. Baur

Keyword(s):

Stock Markets ◽

High Frequency ◽

Realized Volatility ◽

Forecast Horizon ◽

Volatility Asymmetry ◽

Volatility Regimes ◽

The Asymmetry

This paper analyzes high-frequency estimates of good and bad realized volatility of Bitcoin. We show that volatility asymmetry depends on the volatility regime and the forecast horizon. For one-day ahead forecasts, good volatility commands a stronger impact on future volatility than bad volatility on average and in extreme volatility regimes but not across all quantiles and volatility regimes. For 7-day ahead forecasting horizons the asymmetry is similar to that observed in stock markets and becomes stronger with increasing volatility. Compared with stock markets, the persistence and predictability of volatility is low indicating high variations of volatility.

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