On improved volatility modelling by fitting skewness in ARCH models

ABSTRACT

We study ARCH/GARCH effects under possible deviation from normality. Since skewness is the principal cause for deviations from normality in many practical applications, e.g. finance, we study in particular skewness. We propose robust tests for normality both for NoVaS and modified NoVaS transformed and original data. Such an approach is not applicable for EGARCH, but applicable for GARCH-GJR models. A novel test procedure is proposed for the skewness in autoregressive conditional volatility models. The power of the tests is investigated with various underlying models. Applications with financial data show the applicability and the capabilities of the proposed testing procedure.

KEYWORDS:

• Robust test for normality
• ARCH/GARCH model
• NoVaS
• skewness
• kurtosis

Acknowledgements

The authors are very grateful to the Editor, Associated Editor and the Reviewers for their valuable comments.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1. That is, the unconditional joint probability distribution does not change when shifted in time.

2. Furthermore, the strictly stationary solution of (5(5) ${ϵ}_t=\sqrt{h_t}{e}_t\mathrm{and}{h}_t=\omega +\sum _{i=1}^k(a_i+{\eta }_i{\mathbb{I}}_{\{{ϵ}_{t-i}<0\}}){ϵ}_{t-i}^2+\sum _{i=1}^l{\tilde{a}}_i{h}_{t-i},$(5) ) with ${\eta }_i=0$ has the finite fourth moment provided $max\{1,E[e_t^4{]}^{\frac{1}{2}}\}{A}_k/(1-{\tilde{A}}_l)<1$, see e.g. [16, Section 4.2].

Additional information

Funding

M. Stehlík and P. Jordanova acknowledge project FONDECYT Regular No. 1151441 and bilateral projects Bulgaria – Austria, 2016–2019, ‘Feasible statistical modelling for extremes in ecology and finance’, Contract number 01/8, 23/08/2017 and WTZ Project No. BG 09/2017. M. Stehlík and J. KiseĬák acknowledge project LIT-2016-1-SEE-023. L. Střelec acknowledges the support of the Czech Science Foundation (GA CR, project No. GA16-07089S). J. KiseĬák and J. Hudák were also supported by the Slovak Research and Development Agency under the contract No. APVV-17-0568.