Abrupt Structural Changes in Complex Stochastic Systems with Applications to Economics, Finance, and Genetics

Suny At Stony Brook, Stony Brook NY

Investigators

Abstract

Abrupt structural changes in complex stochastic systems arise in science and engineering, including economics, finance, genetics, industrial quality control, and public health. An important step to analyze these problems is to develop appropriate models with parameter jumps and efficient inference procedures. In the proposed research, the principal investigator will investigate three complicated problems with abrupt structural changes that recently arise in three different disciplines and develop corresponding statistical methodology for them. The first is to develop a modulated Markov model with unknown structural breaks to characterize U.S. firms' credit rating transitions when the economy undergoes abrupt structural changes. An inference procedure is also proposed to analyze the relationship between structural changes in the U.S. credit market and variations of macroeconomic and firm-specific covariates. The second is to investigate the issue of learning and control in a sharply changing environment and develop an approximate policy optimization and adaptive control method for the analysis of optimal policies, its application to monetary policy analysis is also discussed. The third problem is to develop a segmentation model that identifies topologically associated domains in the analysis of chromatin interactions, which is an important step in the analysis of the next-generation genome-sequencing data. A statistically and computationally efficient segmentation algorithm is also proposed to estimate the boundaries of topologically associated domains. The PI will show how these challenging problems in different areas can be unified and resolved by the proposed statistical models and inference procedures. Statistical inference problems in complex stochastic systems with abrupt structural changes arise in science and engineering, including economics, finance, risk management, genetics, industrial quality control, and public health. There has been an extensive literature on stochastic systems with simple structural change mechanisms, however, problems of complex stochastic systems with abrupt structural changes have been hampered by their statistical difficulty and hence has not received much attention. In current genetic research, understanding 3D chromosomal structures and chromatin interactions for decoding and interpreting functions of the genome can provide important hints toward decoding the mechanisms of gene regulation and the maintenance of genome stability, as well as DNA replication, repair and modification, an important step in studying these genetic events is to identify the topologically associated domains from chromatin architecture data. In macroeconomic studies, central banks are keen to control the policy target and estimate the impact of policy action simultaneously with the presence of the unobservable economic structural breaks, so that proper monetary and fiscal policies can be taken to mitigate the potential harmful impact of sharp economic turns. In financial studies, the 2008-2009 financial crisis raises the immediate needs for the regulatory authorities that the financial market should be 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 systems. The proposed research explores the possibility of building quantitative and implementable early-warning systems for financial crisis, which aggregates microeconomic information from individual firms and macroeconomic statistics from general economic activities.