On quantiles of the temporal aggregation of a stable moving average process and their applications

Adrian Barker

Abstract


A stochastic volatility model is proposed for the daily log returns of a financial asset based on conditional log quantile differences, assuming the availability of high frequency intraday log returns. Calculation of the conditional log quantile differences is performed with the assumption that the intraday log returns follow a stable moving average process. The use of conditional log quantile difference in the proposed model, rather than conditional variance in standard models, offers an increase in flexibility, with the potential for a different dependency structure at different parts of the conditional distribution. The proposed model makes use of high frequency intraday log returns which are generally neglected in standard models. Formulae for the calculation of the conditional log quantile differences are provided and a method for their estimation is described The proposed model was applied to the ASX200 index from 2009 and 2010.

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Keywords


stable distribution; temporal aggregation; stochastic volatility

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DOI: http://dx.doi.org/10.21914/anziamj.v55i0.7826



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