Analytic moments for GJR-GARCH (1,1) processes

Alexander, C., Lazar, E. ORCID: https://orcid.org/0000-0002-8761-0754 and Stanescu, S. (2021) Analytic moments for GJR-GARCH (1,1) processes. International Journal of Forecasting, 37 (1). pp. 105-124. ISSN 0169-2070 doi: 10.1016/j.ijforecast.2020.03.005

Abstract/Summary

For a GJR-GARCH(1,1) specification with a generic innovation distribution we derive analytic expressions for the first four conditional moments of the forward and aggregated returns and variances. Moments for the most commonly used GARCH models are stated as special cases. We also derive the limits of these moments as the time horizon increases, establishing regularity conditions for the moments of aggregated returns to converge to normal moments. A simulation study using these analytic moments produces approximate predictive distributions which are free from the bias affecting simulations. An empirical study using almost 30 years of daily equity index, exchange rate and interest rate data applies Johnson SU and Edgeworth expansion distribution fitting to our closed-form formulae for higher moments of returns.

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/89679
Identification Number/DOI	10.1016/j.ijforecast.2020.03.005
Refereed	Yes
Divisions	Henley Business School > Finance and Accounting
Publisher	Elsevier
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