Browsing by Author "Mutombo, Pierre Abraham Mulamba"
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- ItemTwo-phase behaviour in a sequence of random variables(Stellenbosch : Stellenbosch University, 2007-03) Mutombo, Pierre Abraham Mulamba; Krzesinski, A. E.; Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences.ENGLISH ABSTRACT: Buying and selling in financial markets are driven by demand. The demand can be quantified by the imbalance in the number of shares QB and QS transacted by buyers and sellers respectively over a given time interval t. The demand in an interval t is given by (t) = QB − QS. The local noise intensity is given by = h|aiqi − haiqii|i where i = 1, . . . ,N labels the transactions in t, qi is the number of shares traded in transaction i, ai = ±1 denotes buyer- initiated and seller- initiated trades respectively and h· · · i is the local expectation value computed from all the transactions during the interval t. In a paper [1] based on data from the New York Stock Exchange Trade and Quote database during the period 1995-1996, Plerou, Gopikrishnan and Stanley [1] reported that the analysis of the probability distribution P( | ) of demand conditioned on the local noise intensity revealed the surprising existence of a critical threshold c. For < c, the most probable value of demand is roughly zero; they interpreted this as an equilibrium phase in which neither buying nor selling predominates. For > c two most probable values emerge that are symmetrical around zero demand, corresponding to excess demand and excess supply; they interpreted this as an out-of-equilibrium phase in which the market behaviour is buying for half of the time, and selling for the other half. It was suggested [1] that the two-phase behaviour indicates a link between the dynamics of a financial market with many interacting participants and the phenomenon of phase transitions that occurs in physical systems with many interacting units. This thesis reproduces the two-phase behaviour by means of experiments using sequences of random variables. We reproduce the two-phase behaviour based on correlated and uncorrelatd data. We use a Markov modulated Bernoulli process to model the transactions and investigate a simple interpretation of the two-phase behaviour. We sample data from heavy-tailed distributions and reproduce the two-phase behaviour. Our experiments show that the results presented in [1] do not provide evidence for the presence of complex phenomena in a trading market; the results are a consequence of the sampling method employed.