The Stationary, Continuous Time, Discrete Space (SCD) Model with Polya Tree for Micro Data Analysis in Finance

• Activity Number: 376
• Type: Contributed
• Date/Time: Tuesday, August 4, 2009 : 2:00 PM to 3:50 PM
• Sponsor: Business and Economic Statistics Section
• Author(s): Masaru Hashimoto*+ and Peter Lenk
• Companies: Mitsubishi UFJ Securities and University of Michigan
• Keywords: Bayesian Nonparametric ; Polya Tree ; Hierarchical Bayes ; Markov Chain Monte Carlo ; Microstructure

Abstract

The stationary, continuous time, discrete space (SCD) model is developed. This paper highlights some aspects of the SCD model. The SCD model, a class of stationary Markov processes, is useful to investigate phenomenon in financial micro data. This model has two components; one component for the inter arrival time, the time of two adjacent transactions, and one component for the transition of a stock price to a new price. The inter arrival time follows the exponential distribution. This paper suggests the model using hierarchical Bayes model via Markov Chain Monte Carlo (MCMC) in the exponential distribution. For the other component, Polya tree, one of the Bayesian nonparametric distributions, estimates the transition probability. The Polya tree estimation is useful for micro data in equity because it induces smoothing "thin data" where there is few or no observation for each state.