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Title: Quantile-based methods for prediction, risk measurement and inference
Author: Ally, Abdallah K.
ISNI:       0000 0004 2702 2234
Awarding Body: Brunel University
Current Institution: Brunel University
Date of Award: 2010
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The focus of this thesis is on the employment of theoretical and practical quantile methods in addressing prediction, risk measurement and inference problems. From a prediction perspective, a problem of creating model-free prediction intervals for a future unobserved value of a random variable drawn from a sample distribution is considered. With the objective of reducing prediction coverage error, two common distribution transformation methods based on the normal and exponential distributions are presented and they are theoretically demonstrated to attain exact and error-free prediction intervals respectively. The second problem studied is that of estimation of expected shortfall via kernel smoothing. The goal here is to introduce methods that will reduce the estimation bias of expected shortfall. To this end, several one-step bias correction expected shortfall estimators are presented and investigated via simulation studies and compared with one-step estimators. The third problem is that of constructing simultaneous confidence bands for quantile regression functions when the predictor variables are constrained within a region is considered. In this context, a method is introduced that makes use of the asymmetric Laplace errors in conjunction with a simulation based algorithm to create confidence bands for quantile and interquantile regression functions. Furthermore, the simulation approach is extended to an ordinary least square framework to build simultaneous bands for quantiles functions of the classical regression model when the model errors are normally distributed and when this assumption is not fulfilled. Finally, attention is directed towards the construction of prediction intervals for realised volatility exploiting an alternative volatility estimator based on the difference of two extreme quantiles. The proposed approach makes use of AR-GARCH procedure in order to model time series of intraday quantiles and forecast intraday returns predictive distribution. Moreover, two simple adaptations of an existing model are also presented.
Supervisor: Yu, K. ; Vinciotti, V. Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: Prediction intervals ; Expected shortfall ; Realised volatility ; Integrated volatility ; Quantile regression confidence bands