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| 說明 | 1 online resource (139 pages) |
| 文字 | text |
| 無媒介 | computer |
| 成冊 | online resource |
| 附註 | Source: Dissertation Abstracts International, Volume: 78-02(E), Section: B |
| Adviser: Beth Andrews |
| Thesis (Ph.D.)--Northwestern University, 2016 |
| Includes bibliographical references |
| This item is not available from ProQuest Dissertations & Theses |
| We propose an integer-valued asymmetric GARCH (INAGARCH) model to describe the conditional heteroscedasticity of stationary integer-valued financial data that are both positive and negative. We use the maximum likelihood estimation methodology to estimate model parameters and derive the asymptotic distribution of the MLE. Diagnostic checking is discussed via conditional squared residuals along with their sample autocovariance function (SACVF). We derive an asymptotic normal distribution for vectors of SACVF values with a specified asymptotic covariance matrix. We standardize the vector of SACVF values by an estimate of its limiting covariance matrix. The standardized SACVF vector is shown to be asymptotically normal and used to examine the goodness-of-fit. Simulation studies are conducted to look at finite sample properties of the MLE and the vector of standardized SACVF values. We fit the INAGARCH model to real integer-valued financial data via MLE and use the standardized SACVF to discuss diagnostic checking. For non-stationary integer-valued financial time series with structural breaks, we use piecewise INAGARCH models to describe data by segmenting the series into several local stationary pieces. We assume the number of break points and their locations are unknown and consider minimum description length (MDL) function for structural break detection. The breaks and INAGARCH parameters are estimated by minimizing MDL values. Estimates are proved to have weak consistency and we use genetic algorithm to automatically obtain these estimates. Numerical simulations are included to examine the consistency of estimates under finite large samples. Finally, we fit piecewise INAGARCH models to a real integer-valued time series and detect possible structural breaks |
| Electronic reproduction. Ann Arbor, Mich. : ProQuest, 2017 |
| Mode of access: World Wide Web |
| 主題 | Statistics |
| Finance |
| Mathematics |
| Electronic books. |
| 0463 |
| 0508 |
| 0405 |
| ISBN/ISSN | 9781369153293 |
