A Parsimonious Multivariate Markov Chain Model for Nse Stocks

Abstract

This study uses the Parsimonious Multivariate Markov chain model to de­ scribe the dependency of transitions of the daily Volume Weighted Average Prices VWAP of Nairobi Securities Exchange prices. The model, unlike the . multivariate Markov chain model, can be used for both positively and neg­ atively associated sequence and has relatively fewer parameters. We consid­ ered 125 daily volume weighted average price (VWAP) values of three stocks (portfolios) 81,82 and 83 in the NSE for a period of 6 months starting 3rd January 2011 to 31st June 2011. From this data we obtained 124 value rates by dividing the VWAP of the day to be calculated with the value of the immediate previous trading day to obtain a three-state (1, 2 and 3 respec­ tively) multivariate Markov chain indicating decrease, no change or increase in price.The transition probability matrices, p(j,i) are estimated through nor­ malization of the transition frequency matrices of the 8 categorical data se­ quences. The model parameters). == {Aj,i} are estimated by minimizing

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