Resumen de The size distortion of the bds distribution in finite sample sizes: A Montecarlo investigation

Julián Andrada Félix, Jorge V. Pérez Rodríguez

• This paper investigates the finite sample distribution of the BDS test based on Monte Carlo simulation in a univariate time series, independent and identically distributed, from a N ( ) 0,1 standard distribution, and proposes a response surface methodology based on an artificial neural network (ANN) to obtain critical values using the experimental results. The ANN depicts a parametric response surface (RS) approximation, instead of the traditional linear regression model, because this makes it possible to approximate the surfaces of complex topology and reveals evidence of more desirable properties. The results obtained highlight the following aspects. Firstly, we find that Monte Carlo critical values are sensitive to the choice of embedding dimension, proximity distance and significance levels in finite samples. Hence, we conclude that the BDS test is characterized by marginal size distortion and departure from normality in finite samples. Secondly, the empirical evidence discussed in this paper suggests that the ANN is a flexible tool to fit the response surface, as a possible alternative to traditional techniques under non-linear contexts, and that it outperforms linear regression models