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

Alexander, Carol, Lazar, Emese and Stanescu, Silvia (2020) Analytic moments for GJR-GARCH (1,1) processes. International Journal of Forecasting. ISSN 0169-2070

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Abstract

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
Schools and Departments: University of Sussex Business School > Accounting and Finance
SWORD Depositor: Mx Elements Account
Depositing User: Mx Elements Account
Date Deposited: 27 Mar 2020 08:46
Last Modified: 19 Jun 2020 15:30
URI: http://sro.sussex.ac.uk/id/eprint/90578

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