| dc.identifier.uri | http://hdl.handle.net/11401/76593 | |
| dc.description.sponsorship | This work is sponsored by the Stony Brook University Graduate School in compliance with the requirements for completion of degree. | en_US |
| dc.format | Monograph | |
| dc.format.medium | Electronic Resource | en_US |
| dc.language.iso | en_US | |
| dc.publisher | The Graduate School, Stony Brook University: Stony Brook, NY. | |
| dc.type | Dissertation | |
| dcterms.abstract | The generalized conditional heteroscedastic (GARCH) models are often used to estimate volatility in financial markets as they mimic the patterns in real world with volatility clustering as well as high excess kurtosis. However, in applications to asset return series, they usually possess undesired persistence in volatility, which can be explained by structure changes in parameters associated with significant economic events such as financial crises. From this motivation, we provide an estimation procedure for multiple parameter changes in GARCH models. By introducing the specified forward and backward filtration and combining them with Bayes' theorem, our estimation procedure has attractive statistical and computational properties and yields explicit recursive formulas to provide semi-parametric estimates for the piecewise constant parameters. Based on the estimates given above with the quasi-likelihood of our model and the modified Bayesian information criterion (MBIC), we also develop a segmentation procedure to give inference on the number and locations of the change-points that partition the unknown parameter sequence into segments of equal values. Furthermore, we propose an expectation-maximization (EM) algorithm to estimate the change-points probability $p$ in our model. Simulation studies are used to compare our performance to the existing procedure and the ``oracle'' estimates, which assume that the change-points are already known. The mean Euclidean error (EE), the Kullback–Leibler divergence (KL), the goodness of fit and the accuracy rate of the numbers of change-points detected are given. Finally, illustrative applications to the S&P 500 index and the IBM stock returns are shown to give an insight how our estimation results coincide with the real financial crises. | |
| dcterms.abstract | The generalized conditional heteroscedastic (GARCH) models are often used to estimate volatility in financial markets as they mimic the patterns in real world with volatility clustering as well as high excess kurtosis. However, in applications to asset return series, they usually possess undesired persistence in volatility, which can be explained by structure changes in parameters associated with significant economic events such as financial crises. From this motivation, we provide an estimation procedure for multiple parameter changes in GARCH models. By introducing the specified forward and backward filtration and combining them with Bayes' theorem, our estimation procedure has attractive statistical and computational properties and yields explicit recursive formulas to provide semi-parametric estimates for the piecewise constant parameters. Based on the estimates given above with the quasi-likelihood of our model and the modified Bayesian information criterion (MBIC), we also develop a segmentation procedure to give inference on the number and locations of the change-points that partition the unknown parameter sequence into segments of equal values. Furthermore, we propose an expectation-maximization (EM) algorithm to estimate the change-points probability $p$ in our model. Simulation studies are used to compare our performance to the existing procedure and the ``oracle'' estimates, which assume that the change-points are already known. The mean Euclidean error (EE), the Kullback–Leibler divergence (KL), the goodness of fit and the accuracy rate of the numbers of change-points detected are given. Finally, illustrative applications to the S&P 500 index and the IBM stock returns are shown to give an insight how our estimation results coincide with the real financial crises. | |
| dcterms.available | 2017-09-20T16:50:45Z | |
| dcterms.contributor | Xing, Haipeng | en_US |
| dcterms.contributor | Wu, Song | en_US |
| dcterms.contributor | Chen, Xinyun | en_US |
| dcterms.contributor | Fang, Yixin. | en_US |
| dcterms.creator | Zhou, Sichen | |
| dcterms.dateAccepted | 2017-09-20T16:50:45Z | |
| dcterms.dateSubmitted | 2017-09-20T16:50:45Z | |
| dcterms.description | Department of Applied Mathematics and Statistics. | en_US |
| dcterms.extent | 108 pg. | en_US |
| dcterms.format | Application/PDF | en_US |
| dcterms.format | Monograph | |
| dcterms.identifier | http://hdl.handle.net/11401/76593 | |
| dcterms.issued | 2015-12-01 | |
| dcterms.language | en_US | |
| dcterms.provenance | Made available in DSpace on 2017-09-20T16:50:45Z (GMT). No. of bitstreams: 1
Zhou_grad.sunysb_0771E_12464.pdf: 1921896 bytes, checksum: b9e170779985e5a956c3b08b890bfe49 (MD5)
Previous issue date: 1 | en |
| dcterms.publisher | The Graduate School, Stony Brook University: Stony Brook, NY. | |
| dcterms.subject | Statistics | |
| dcterms.subject | change-points estimation, empirical Bayesian, GARCH model, parameter change | |
| dcterms.title | Multiple Change-Points Estimation in GARCH Models | |
| dcterms.type | Dissertation | |
