Testing nonlinear dependence in Czech stock index PX50 returns

Efficient Market Hypothesis(EMH) postulates that asset prices are rationally connected to economic realities and always incorporate all the information available to the market. This concept has dominated quantitative capital market theory until recently. On one hand, a great number of studies support this hypothesis. On the other hand. there are plenty of evidence suggesting that financial markets are not efficient. Although most of the empirical tests of the efficient markets hypothesis are based on linear models. a huge quantity of theoretical works around the world have been devoted to nonlinear processes (they can be both stochastic or deterministically chaotic) because these processes can generate output that is similar to the output of linear stochastic systems, hence it may offer an alternative explanation for the behaviour of asset prices. In this paper, the existence of nonlinear dependence on Czech stock index PX50 returns will be examined. Nonlinear dependence may occur in a financial time series even though we have rejected the presence of linear dependence in it. Using daily observation for period 1997 to 2005 (exactly from January 1, 1997 to September 20, 2005, totally 2270 observations). some nonlinearity tests are carried out in order to decide if we can accept the weak form of efficient markets hypothesis. First, the BIDS test will be used to test the general presence of nonlinearity (either stochastic or deterministically chaotic). Secondly, several tests will be used to verify nonlinearity of a time series in its first (White test), second (Engle's test), and third moment (Hinich bispectrum). Finally, in order to test for chaos. two variables will be examined. The fractal nature of a possibly underlying strange attractor of the time series will be measured by estimating its correlation dimension. Computing the largest Lyapunov exponent, the sensitive dependence on initial conditions. a characteristic feature of a chaotic system, will be shown. The results of these tests seem to come to the conclusion that a nonlinear dependence does really, exist in the daily Czech stock index PX50 returns.