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Analytic Moments for GARCH Processes

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  • Carol Alexander
  • Emese Lazar
  • Silvia Stanescu

Abstract

For a GJR-GARCH specification with a generic innovation distribution we derive analytic expressions for the first four conditional moments of the forward and aggregated returns and variances. Moment for the most commonly used GARCH models are stated as special cases. We also the limits of these moments as the time horizon increases, establishing regularity conditions for the moments of aggregated returns to converge to normal moments. Our empirical study yields excellent approximate predictive distributions from these analytic moments, thus precluding the need for time-consuming simulations.

Suggested Citation

  • Carol Alexander & Emese Lazar & Silvia Stanescu, 2018. "Analytic Moments for GARCH Processes," Papers 1808.09666, arXiv.org, revised Sep 2018.
    • Handle: RePEc:arx:papers:1808.09666
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    Cited by:

    1. Alexander, Carol & Lazar, Emese & Stanescu, Silvia, 2013. "Forecasting VaR using analytic higher moments for GARCH processes," International Review of Financial Analysis, Elsevier, vol. 30(C), pages 36-45.
    2. Carol Alexander & Emese Lazar & Silvia Stanescu, 2011. "Analytic Approximations to GARCH Aggregated Returns Distributions with Applications to VaR and ETL," ICMA Centre Discussion Papers in Finance icma-dp2011-08, Henley Business School, University of Reading.

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    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods

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