This dissertation, "On Some Nonlinear Time Series Models and the Least Absolute Deviation Estimation" by Guodong, Li, 李國棟, was obtained from The University of Hong Kong (Pokfulam, Hong Kong) and is being sold pursuant to Creative Commons: Attribution 3.0 Hong Kong License. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation. All rights not granted by the above license are retained by the author. Abstract: Abstract of thesis entitled ON SOME NONLINEAR TIME SERIES MODELS AND THE LEAST ABSOLUTE DEVIATION ESTIMATION Submitted by LI GUODONG for the degree of Doctor of Philosophy at The University of Hong Kong in June 2007 This study investigated some testing and estimating problems for time series models with conditional heteroscedasticity. Some new statistical tools were de- velopedwhichmightprovidenewinsightsintotheunderstandingofnancialand economic time series. Empirical evidences showed that many nancial and economic data may be heavy-tailed and, as a robust statistical approach, the least absolute deviation estimation had recently become popular in the modeling of time series exhibiting this phenomenon. Two useful diagnostic tools, based on the asymptotic distribu- tions of absolute residual autocorrelations and squared residual autocorrelations, weredevelopedinthisthesistocheckwhetherageneralizedautoregressivecondi- tional heteroscedastic (GARCH) model estimated by the least absolute deviationmethod was adequate or not. Secondly, as the long memory property was known tobepresentinsomeabsolutereturnsequencesinnanceandeconomics, besides heavy tails and time varying conditional variance, a least absolute deviation ap- proachwasdevelopedtoestimatethisphenomenonbasedonthefractionallyinte- grated autoregressive moving average models with conditional heteroscedasticity. Statisticalpropertiesfortheestimatorssuchaslocalasymptoticnormalitieswere derived. Thirdly, as the phenomena of unit roots and heavy tails usually coexist in the same time series, it was clearly necessary to construct a powerful test to identify the presence of unit roots under heavy tails. A least absolute deviation estimation was considered for the unit root processes with GARCH errors, and severalrobustunitroottestswerederivedbasedonthisestimation. Fourthly, the threshold model has become a standard class of nonlinear time series models. An important problem in this literature was to test whether a threshold time series model provided a better t to the real data than a model without a threshold. A quasi-likelihood ratio test was therefore designed to check for the existence of the threshold structure in moving average models under changing conditional variance. MonteCarloexperimentswereconductedtodemonstratetheusefulnessofthe theoriesandmethodsdevelopedabove. ApplicationstotheHangSengIndex, the Dow Jones Industrial Average Index, the S&P 500 index and the exchange rate of Japanese Yen and US dollar provided some new insights into these time series. DOI: 10.5353/th_b3878239 Subjects: Heteroscedasticity Time series analysis