Doctoral Dissertations

Abstract

"The two of the main formulations for modeling long range dependence in volatilities associated with financial time series are fractionally integrated generalized autoregressive conditional heteroscedastic (FIGARCH) and hyperbolic generalized autoregressive conditional heteroscedastic (HYGARCH) models. The traditional methods of constructing prediction intervals for volatility models, either employ a Gaussian error assumption or are based on asymptotic theory. However, many empirical studies show that the distribution of errors exhibit leptokurtic behavior. Therefore, the traditional prediction intervals developed for conditional volatility models yield poor coverage. An alternative is to employ residual bootstrap-based prediction intervals. One goal of this dissertation research is to develop methods for constructing such prediction intervals for both returns and volatilities under FIGARCH and HYGARCH model formulations.

In addition, this methodology is extended to obtain prediction intervals for autoregressive moving average (ARMA) and fractionally integrated autoregressive moving average (FARIMA) models with a FIGARCH error structure. The residual resampling is done via a sieve bootstrap approach, which approximates the ARMA and FARIMA portions of the models with an AR component. AIC criteria is used to find order of the finite AR approximation on the conditional mean process. The advantage of the sieve bootstrap method is that it does not require any knowledge of the order of the conditional mean process. However, we assume that the order of the FIGARCH part is known. Monte- Carlo simulation studies show that the proposed methods provide coverages closed to the nominal values"--Abstract, page iv.

Advisor(s)

Samaranayake, V. A.

Committee Member(s)

Adekpedjou, Akim
Olbricht, Gayla R.
Paige, Robert L.
Gelles, Gregory M.

Department(s)

Mathematics and Statistics

Degree Name

Ph. D. in Mathematics

Comments

Doctor of Philosophy in Mathematics with Statistics emphasis

Publisher

Missouri University of Science and Technology

Publication Date

Spring 2021

Journal article titles appearing in thesis/dissertation

  • Bootstrap prediction intervals for fractionally integrated generalized autoregressive conditional heteroscedastic (FIGARCH) models
  • Sieve bootstrap-based prediction intervals for ARMA models with fractionally integrated generalized autoregressive conditional heteroscedastic (FIGARCH) errors
  • Sieve bootstrap-based prediction intervals for FARIMA-FIGARCH models
  • Bootstrap prediction intervals for hyperbolic generalized autoregressive conditional heteroscedastic (HYGARCH) models

Pagination

xv, 132 pages

Note about bibliography

Includes bibliographic references.

Rights

© 2021 Ekanayake Mudiyanselage Rukman Sumedha Ekanayake, All rights reserved.

Document Type

Dissertation - Open Access

File Type

text

Language

English

Thesis Number

T 11833

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