Stock market modelling using markov chain analysis

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Technická Univerzita v Liberci
Technical university of Liberec, Czech Republic
Price reduction and increased computation performance as well as the development of electronic databases bring new possibilities for analysing and predicting stock markets. This study is focused on modelling share price changes using Markov chain analysis (MCA). The aim of the study is to analyse the possibilities of MCA usage for construction of technical analysis (TA) indicators. The study is based on the data from the Prague Stock Exchange in the space of 7 years from 2 January 2006 until 2 January 2010, specifically for the close daily prices of the following shares: ČEZ, Komerční Banka and Telefonica O2. Out of these close prices the share price daily change and the share price cumulated change for a certain period of time have been calculated. The length of time period has been determined by the number of growing or decreasing close prices in sequence. According to daily and cumulated share price changes three models with different discreet state spaces have been defined. For each model we have calculated the number of individual states, the conditioned probabilities of transition between particular states and conditioned probabilities of transition into growing and decreasing states. Calculations have been carried out in MS Excel using algorithm programmed in VBA. Gained results show that for a conveniently defined state space, models based on MCA could be usable for TA. Making use of these models for construction of TA indicators will be the objective of other research.
Markov chain analysis, transition probability matrix, trend prediction, time series analysis, technical analysis