Indexed Markov Chains for financial data: testing for the number of\n states of the index process

2018/02/05 by Guglielmo D’Amico, D'Amico, Guglielmo, Ada Lika +3
Computer Science · Economics, Econometrics and Finance · #Advanced Database Systems and Queries #Complex Systems and Time Series Analysis #Data Management and Algorithms #FOS: Economics and business #Statistical Finance (q-fin.ST)

paper · pdf · doi:10.48550/arxiv.1802.01540

openalex publication_date 2018/02/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A new branch based on Markov processes is developing in the recent literature\nof financial time series modeling. In this paper, an Indexed Markov Chain has\nbeen used to model high frequency price returns of quoted firms. The\npeculiarity of this type of model is that through the introduction of an Index\nprocess it is possible to consider the market volatility endogenously and two\nvery important stylized facts of financial time series can be taken into\naccount: long memory and volatility clustering. In this paper, first we propose\na method for the optimal determination of the state space of the Index process\nwhich is based on a change-point approach for Markov chains. Furthermore we\nprovide an explicit formula for the probability distribution function of the\nfirst change of state of the index process. Results are illustrated with an\napplication to intra-day prices of a quoted Italian firm from January 1^st,\n2007 to December 31^st 2010.\n

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