Methodology for detection of determinism and nonlinearity on financial time series

• Luz Ospina Universidad Tecnológica de Pereira-Colombia
• José Soto Universidad Tecnológica de Pereira-Colombia
• ílvaro Orozco Universidad Tecnológica de Pereira-Colombia
• John Escobar Universidad Javeriana- Colombia

Palabras clave: financial time series, irregular fluctuations, nonlinear dynamical system, surrogate data, hypothesis testing

Resumen

This paper uses the method of surrogate data to analyze the dynamics of financial time signals suggesting a hierarchy of hypotheses where irregular fluctuations: (i) are independently distributed, (ii) are generated by a linear system, and (iii) are generated by a stationary linear system. These hypotheses are tested with a battery of non-linear statistical: (i) Autocorrelation (AC), (ii) Average Mutual Information (AMI) and (iii) the complexity of Lempel-Ziv. In this work, we have compared the behavior of the original signal with a set of surrogate data generated, which satisfies the assumptions of the non-linear statistics. The result is useful for understanding the nature of the data and to formulate models that best fit the dynamics of systems that generate measurements. Computational experiments on the commodity gold show that the series could follow a dynamic different to the “white noise” with nonlinearity characteristics and non-stationary condition. Therefore, it is possible to determine that in modeling the price of the gold could be possible to exclude several proposed mathematical models, which no consider these characteristics