Non linearities and chaos in stock price behavior of Greek oil sector; The case of Hellenic Petroleum S.A.

The behaviour of different financial or economic time series is captured mainly by
nonlinear models. The present study investigates the underlying process of the stock
price returns time series of the oil sector taking as an example the case of Hellenic
Petroleum SA. The data used are daily for over a 13 – year period. Nonlinearities are
detected with different univariate tests that survey the independence and nonlinear
deterministic structure of the time series studied. The data employed for these tests are
the closing prices of Hellenic Petroleum SA. All the tests confirm the existence of
nonlinearities in the time series studied. Furthermore, we employ a Layapunov test to
detect the chaotic behaviour of the stock prices. Finally, we estimate the noisy
Mackey – Glass model, which is an equation with errors that follow an F- GARCH (p,
q) process. This model is structured in order to enable us to interpret the volatility
clustering as an endogenous phenomenon.