Statistical inference problems in complex stochastic systems with parameter jumps arise in science and engineering, including economics, finance, genetics, industrial quality control, and public health. An important ingredient in the solution to these problems is efficient estimation of time-varying parameters with unknown jumps. In the proposed research, the investigator studies some newly emerged stochastic models with unknown parameter jumps in different disciplines and develops the related inference procedure. In particular, four types of problems in different areas are studied in the proposal. The first investigates a semi-parametric change-point regression model and its inference procedure for abrupt changes of covariate effect in longitudinal studies. The second develops a credit rating transition model in the presence of unknown structural breaks and an estimation procedure for the analysis of the relationship between the structural breaks in the U.S. credit market and macroeconomic and firm-specific covariates. The third considers a class of Markov switching models with stochastic regimes and their applications in economic analysis of business cycles and recurrent copy number variation analysis in genomic studies. The fourth problem discusses surveillance rules in sequential surveillance problems and their applications in risk management. The investigator will show how these challenging problems in different areas can be unified and solved by the developed statistical models and inference procedures.
Complex stochastic systems with unknown parameter jumps are often encountered in various scientific and engineering practices including economics, finance, biology, risk management and control. While systems with smoothly changing parameters have been discussed intensively in the literature, recent advances in natural and social sciences show the growing importance of stochastic systems with unknown parameter jumps. In current genomic research, DNA copy number variations are key genetic events in the development and progression of numerous diseases including cancer, HIV acquisition, and Alzheimer and Parkinson's disease, and an important step in studying these genetic events is to identify the regions of variations. In economic studies, the authorities are keen to have a more detailed and quantitative characterization of the real economic states, instead of some simple descriptions such as booming or recession that are commonly discussed in the economic literature, so that proper monetary and fiscal policies can be issued. In financial studies, the 2008-2009 financial crisis raises the immediate needs for the regulatory authorities that the credit market and banking systems should be regulated and monitored based on solid statistical and econometric models and procedures, and hence an early warning system should be established to surveillance the stability of financial and economic systems. The proposed research is one of the first attempts to explore the possibility of building quantitative and implementable early-warning systems for financial markets and economic activities, which aggregates microeconomic information among individual firms and banks and macroeconomic statistics from general economic activities.
