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This paper advances Multilevel Stochastic Dynamic Process (MSDP) models as a new framework for modelling nonstationary and nonlinear time series and complex systems, and discuss possible applications of MSDP models in global financial market analysis and surveillance. Both the discreteand continuous-time forms of MSDP models are constructed: Multilevel Structural Time Series (MSTS) with Unobserved Components (UC) and Multilevel Stochastic Differential Equations (MSDE). On possible applications of MSDP models, attention is focused on the two most important types of financial markets: world major stock market indices and global foreign exchange (forex) rates. Based on MSDP models, a comprehensive methodology for financial market analysis and surveillance is provided, which consists of three major components: (1) developing a particular set of MSDP models for a given set of markets, (2) identification of multilevel trends, cycles and seasonalities using particular models, (3) discovery, detection and projection of high-level dynamics patterns including turbulence and chaos, convergence of multiple time frames signalling market crashes or trend accelerations, and financial bubbles and anti-bubbles. Managing financial market and currency risks with robust scientific models is extremely important for governments and corporations. MSDP models for stock markets and forex markets will enable governments and financial industry to implement market surveillance for early warning on financial market crises, and provide pockets of predictability on multiple time frames for making better decisions involving international stock and currency portfolios. MSDP models as a general and powerful mathematical and computational modelling framework have a potential to create a new generation of multilevel stochastic dynamical process models not only in finance but also in social, economical, natural, environmental, physical and engineering applications.

Multilevel Stochastic Dynamic Process Models and Possible Applications in Global Financial Market Analysis and Surveillance