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dc.contributor.authorChan, Felix
dc.contributor.editorLes Oxley
dc.contributor.editorDon Kulasiri
dc.identifier.citationChan, F. 2007. An example on modelling conditional higher moments using maximum entropy density with high frequency data, in Oxley, L. and Kulasiri, D. (ed), MODSIM 2007 International Congress on Modelling and Simulation, Dec 10 2007, pp. 2034-2040. Christchurch, New Zealand: Modelling and Simulation Society of Australia and New Zealand.

Since the introduction of the Autoregressive Conditional Heteroscedasticity (ARCH) model of Engle (1982), the literature of modelling the conditional second moment has become increasingly popular in the last two decades. This popularity is reflected by the numerous volatility models being proposed in the literature and their multivariate counterparts (see McAleer (2005)) for an excellent survey on the various volatility models and related issues on estimation and specification). Interestingly, the Quasi Maximum Likelihood Estimator (QMLE) with normal density is typically used to estimate the parameters in these models. As such, the higher moments of the underlying distribution are assumed to be the same as the normal distribution. However, various studies reveal that the higher moments, such as skewness and kurtosis of the distribution of financial returns are not likely to be the same as the normal distribution, and in some cases, they are not even constant over time. This has significant implications in risk management, especially in the calculation of Value-at-Risk (VaR), which focuses on the negative quantile of the return distribution. Failed to accurately capture the shape of the negative quantile, which is determined by the skewness and the kurtosis of the distribution, would produce inaccurate measure of risk, and subsequently lead to misleading decision in risk management.This paper proposes a general framework to model the distribution of financial returns using Maximum Entropy Density (MED). The main advantage of MED is that it provides a general framework to estimate the distribution function directly based on a given set of data, and it provides a convenient framework to model higher order moments up to any arbitrary finite order k. However this flexibility comes with a high cost in computation time ask increases, therefore this paper proposes an alternative model that would reduce computation time substantially. Moreover, the sensitivity of the parameters in the MED with respect to the dynamic changes of moments is derived analytically. This result is important as it relates the dynamic structure of the moments to the parameters in the MED. The usefulness of this approach will be demonstrated using 5 minutes intra-daily returns of the Euro/USD exchange rate. 2034

dc.publisherModelling & Simulation Society of Australia & New Zealand Inc.
dc.titleAn example on modelling conditional higher moments using maximum entropy density with high frequency data.
dc.typeConference Paper
dcterms.source.titleProceedings of the 2007 international congress on modelling simulation
dcterms.source.seriesProceedings of the 2007 international congress on modelling simulation
dcterms.source.conferenceInternational Congress on Modelling and Simulation
dcterms.source.conference-start-dateDec 10 2007
dcterms.source.conferencelocationChristchurch, New Zealand
dcterms.source.placeNew Zealand
curtin.departmentSchool of Economics and Finance
curtin.accessStatusFulltext not available

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