Stat Colloquium: Dr. Tirupathi Rao Padi

Title: Stochastic Modeling and Statistical Intelligence for Dynamic Financial Systems: Markov and Hidden Markov Approaches

Abstract: Financial markets constitute complex dynamic systems characterized by volatility, uncertainty, non-linearity, and evolving dependence structures. These characteristics create substantial challenges for statistical modeling, forecasting, risk assessment, and evidence-based decision-making. Stochastic modeling provides a natural framework for representing such uncertainty by describing alternative future outcomes together with their associated probabilities. In particular, Markov Chain Models (MCMs) and Hidden Markov Models (HMMs) offer powerful probabilistic frameworks for analyzing temporal state transitions, latent market regimes, and observable financial movements.

This invited lecture will present a research-oriented framework for stochastic modeling of dynamic financial systems, with particular emphasis on the development, statistical interpretation, and empirical application of Markov and Hidden Markov models. The discussion will begin with the foundations of stochastic processes and the Markov property, followed by the formulation of transition probability matrices, initial probability vectors, higher-order transition probabilities, stationary and steady-state distributions, expected state visits, and expected return times. The research framework further considers the derivation of probability distributions for different state sequences, along with their corresponding descriptive statistics and generating functions.

A major component of the lecture will focus on the transition from observable-state Markov modeling to latent-state modeling through HMMs. HMMs provide a framework in which the underlying state process is not directly observable, while the available data arise through an associated observation or emission process. This distinction is particularly relevant in financial markets, where observed price movements may be driven by unobserved economic, behavioural, institutional, and market-regime factors. The empirical component will illustrate how two-state and three-state Markov models can be formulated for financial market movements and calibrated using historical daily closing price data.

The attached research demonstrates applications to Nifty Bank and State Bank of India (SBI) data, including the estimation of model parameters, steady-state probabilities, expected numbers of visits, expected return times, and short- and long-run forecasting of stock price movements. Beyond stock-market prediction, the lecture will explore the broader research potential of stochastic processes as an interdisciplinary statistical technology. The mathematical-finance perspective naturally integrates probability theory, stochastic processes, statistical modeling, computational statistics, numerical methods, data analytics, and scientific computing. This creates opportunities to extend Markov and Hidden Markov frameworks to regime-switching models, multistate stochastic systems, uncertainty quantification, financial risk modeling, portfolio analytics, and data-driven decision systems. A central objective of the interaction with researchers at the University of Maryland will therefore be to identify common research interests and formulate collaborative projects involving theoretical development, computational implementation, real-time data acquisition, model validation, and application-oriented statistical inference.

Particular attention will be given to developing generalized, higher-dimensional MCM/HMM frameworks, deriving analytically tractable probability distributions and statistical characteristics, integrating computational and data-driven approaches, and validating the proposed models against real-world financial and other dynamic-system datasets. The research material already identifies generalized Markov models and generalized (n\times m) HMMs as important directions for further development.

The proposed lecture is consequently intended not only to communicate a body of research but also to serve as a platform for research dialogue and collaboration between researchers in Statistics and allied disciplines. The ultimate goal is to explore how stochastic modeling can evolve from conventional forecasting into a broader framework of statistical intelligence for understanding, predicting, and managing complex dynamic systems under uncertainty.