Doctoral Dissertations

Keywords and Phrases

Asymmetry in volatility; GARCH-type models; Long- and short-term memory in volatility; Mixture memory; Smooth transition; Threshold model


"The volatility of asset returns is usually time-varying, necessitating the introduction of models with a conditional heteroskedastic variance structure. In this dissertation, several existing formulations, motivated by the Generalized Autoregressive Conditional Heteroskedastic (GARCH) type models, are further generalized to accommodate more dynamic features of asset returns such as asymmetry, long memory, and structural breaks. First, we introduce a hybrid structure that combines short-memory asymmetric Glosten, Jagannathan, and Runkle (GJR) formulation and the long-memory fractionally integrated GARCH (FIGARCH) process for modeling financial volatility. This formulation not only can model volatility clusters and capture asymmetry but also considers the characteristic of long memory in the volatility. In the second paper, we extend the Hybrid GJR and FIGARCH process to allow for a graduate transition between two regimes by introducing a smooth transition function. Here, the model changes smoothly between the extremes of the asymmetric short and long memory components depending on a transition variable. The third paper proposes a regime-switching asymmetric long memory model, Multiple Regime Hyperbolic GARCH (MR-HYGARCH), where the regime of an asset return is determined by observing asymmetry between positive and negative returns in its past long-term and past short-term periods. Firstly, it introduces a customizable multiple regime switching mechanism, allowing for tailored modeling according to specific problem requirements. Secondly, it proposes a new specification featuring four regimes governed by a dynamic threshold, in contrast to existing threshold GARCH models that rely on a fixed threshold with only two regimes. Finally, a multiplicative component process (MF)2EGARCH that models the conditional variance as the product of a short-term volatility component, modeled as an exponential GARCH (EGARCH) process and a long-term component, is introduced. Overall, the proposed models demonstrate superior performance compared to their respective competing models in both in-sample estimation and out-of-sample forecasting capabilities"--Abstract, p. iv


Samaranayake, V. A.

Committee Member(s)

Gelles, Gregory M.
Olbricht, Gayla R.
Paige, Robert L.
Wen, Xuerong Meggie


Mathematics and Statistics

Degree Name

Ph. D. in Mathematics and Statistics


Missouri University of Science and Technology

Publication Date

Summer 2023


xiv, 179 pages

Note about bibliography

Includes_bibliographical_references_(pages 169-178)


© 2023 K. C. M. R. Anjana Bandara Yatawara, All Rights Reserved

Document Type

Dissertation - Open Access

File Type




Thesis Number

T 12305

Electronic OCLC #