Time operator of Markov chains and mixing times. Applications to financial data

I. Gialampoukidis, K. Gustafson and I. Antoniou

Physica A: Statistical Mechanics and its Applications, 2014, vol. 415, issue C, 141-155

Abstract: We extend the notion of Time Operator from Kolmogorov Dynamical Systems and Bernoulli processes to Markov processes. The general methodology is presented and illustrated in the simple case of binary processes. We present a method to compute the eigenfunctions of the Time Operator. Internal Ages are related to other characteristic times of Markov chains, namely the Kemeny time, the convergence rate and Goodman’s intrinsic time. We clarified the concept of mixing time by providing analytic formulas for two-state Markov chains. Explicit formulas for mixing times are presented for any two-state regular Markov chain. The mixing time of a Markov chain is determined also by the Time Operator of the Markov chain, within its Age computation. We illustrate these results in terms of two realistic examples: A Markov chain from US GNP data and a Markov chain from Dow Jones closing prices. We propose moreover a representation for the Kemeny constant, in terms of internal Ages.

Keywords: Time Operator; Internal Age; Markov chains; Mixing time; Kemeny constant (search for similar items in EconPapers)
Date: 2014
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:415:y:2014:i:c:p:141-155

DOI: 10.1016/j.physa.2014.07.084

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