University of Sussex
Browse
1/1
2 files

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

journal contribution
posted on 2023-06-09, 20:58 authored by Carol AlexanderCarol Alexander, Emese Lazar, Silvia Stanescu
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.

History

Publication status

  • Published

File Version

  • Accepted version

Journal

International Journal of Forecasting

ISSN

0169-2070

Publisher

Elsevier

Issue

1

Volume

37

Page range

105-124

Department affiliated with

  • Accounting and Finance Publications

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2020-03-27

First Open Access (FOA) Date

2022-04-05

First Compliant Deposit (FCD) Date

2020-03-26

Usage metrics

    University of Sussex (Publications)

    Categories

    No categories selected

    Exports

    RefWorks
    BibTeX
    Ref. manager
    Endnote
    DataCite
    NLM
    DC