One of the essential features of financial time series data is volatility. It is often the case that, over time, structural changes occur in volatility, and an accurate estimation of the volatility of financial time series requires careful identification of the change-points. A common approach to modeling the volatility of time series data is based on the well-known Generalized Autoregressive Conditional Heteroscedastic (GARCH) model. Although the problem of change-point estimation of volatility dynamics derived from the GARCH model has been considered in the literature, these approaches rely on parametric assumptions of the conditional error distribution, which are frequently violated in financial time series. This misspecification of error distribution may lead to change-point detection inaccuracies, resulting in unreliable GARCH volatility estimates. In this dissertation, we introduce novel change-point detection algorithms based on a semiparametric GARCH model. The proposed semiparametric GARCH model retains the structural advantages of the GARCH process while incorporating the flexibility of nonparametric conditional error distribution. Consequently, the likelihood function and the corresponding volatility estimates obtained via this semiparametric approach are more accurate than the traditional Quasi-Maximum Likelihood Estimation (QMLE) method that relies on an assumed parametric error distribution.
The main objective of the change-point estimation problem is to detect the exact number and locations of the change-points. This dissertation proposes an innovative semiparametric GARCH process in developing solutions for change-point estimation problems. Specifically, a penalized likelihood approach based on a semiparametric GARCH model and an efficient binary segmentation algorithm is developed to estimate the change points' locations. The results demonstrate that in terms of change-point identification and estimation accuracy for multiple GARCH process variations, the proposed semiparametric method outperforms the commonly used approaches to change-point analysis in financial data.
| Identifer | oai:union.ndltd.org:bu.edu/oai:open.bu.edu:2144/43180 |
| Date | 07 October 2021 |
| Creators | Hu, Huaiyu |
| Contributors | Gangopadhyay, Ashis |
| Source Sets | Boston University |
| Language | en_US |
| Detected Language | English |
| Type | Thesis/Dissertation |
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