Mathematical and Statistical Methods for Actuarial Sciences and Finance

Financial time series and neural networks in a

minority game context

Luca Grilli, Massimo Alfonso Russo, and Angelo Sfrecola

Abstract.In this paper we consider financial time series from U.S. Fixed Income Market,

S&P500, DJ Eurostoxx 50, Dow Jones, Mibtel and Nikkei 225. It is well known that financial

time series reveal some anomalies regarding the Efficient Market Hypothesis and some scaling

behaviour, such as fat tails and clustered volatility, is evident. This suggests that financial time

series can be considered as “pseudo”-random. For this kind of time series the prediction power

of neural networks has been shown to be appreciable [10]. At first, we consider the financial

time series from the Minority Game point of view and then we apply a neural network with

learning algorithm in order to analyse its prediction power. We prove that the Fixed Income

Market shows many differences from other markets in terms of predictability as a measure of

market efficiency.

Key words:Minority Game, learning algorithms, neural networks, financial time series, Ef-

ficient Market Hypothesis

1 Minority games and financial markets

At the very beginning of the last century Bachelier [2] introduced the hypothesis

that price fluctuations follow a random walk; this resulted later in the so-called Effi-

cient Market Hypothesis (EMH). In such markets arbitrages are not possible and so

speculation does not produce any gain. Later, empirical studies showed that the im-

plications of EMH are too strong and the data revealed some anomalies. Even though

these anomalies are frequent, economists base the Portfolio Theory on the assumption

that the market is efficient. One of the most important implications of EMH is the

rationality of all agents who are gain maximisers and take decisions considering all

the information available (which have to be obtained easily and immediately) and in

general do not face any transaction costs. Is it realistic? The huge literature on this

subject shows that an answer is not easy but in general some anomalies are present in

the market. One of the main problems is rationality; as a rule, agents make satisfac-

tory choices instead of optimal ones; they are not deductive in making decisions but

inductive in the sense that they learn from experience. As a consequence, rationality

hypothesis is often replaced by the so-called “Bounded Rationality”; see [13] for

M. Corazza et al. (eds.), Mathematical and Statistical Methodsfor Actuarial Sciencesand Finance
© Springer-Verlag Italia 2010