Using The Probabilistic Fractal Dimension to Decide if a Time Series is Chaotic

In this paper, we use several ways to distinguish between the deterministic time series and stochastic white noise by using correlation exponent test and the BDS test ( Brock Deckert Scheinkman ) ,through simulating a large number of data for testing the efficiency of these methods on several different models.We found that the correlation exponent tests can distinguish white noise from chaos, however it can not distinguish a white noise from a chaotic process mixed with small a mount of white noise .By putting a white noise as the null hypothesis the BDS test rejects the null hypothesis when the data came from from stochastic source.