Teste para verificação da hipótese de ruído branco utilizando teoria da informação

Abstract

We want to verify if sequences of observations are white noise in the plane (H £C). In the literature, we find several works that do this in an “ad hoc” way, checking if the characteristic point of a sequence in that plane is close to the point (1,0). However, as Bandt (2017) states, we do not found detailed analyzes to assign statistical significance to such statements. To elucidate this question, and in the face of the impossibility of counting infinitely long sequences that are guaranteed to be white noise, we gather candidate sequences from three different sources: two physical and one algorithmic considered as a good source. We checked, if we may consider them ideals for our purposes. We analyze the dispersion of the characteristic points of these sequences in the plane (H £C) using four factors: the size of the sequence (N), the size of the word (D), the delay (¿) and the generating source, observing the distance from the characteristic points to the reference point. We observe that the generating source would be an irrelevant factor to the analyses. To verify this hipothesis, we applied the Kolmogorov-Smirnov test to pairs of comparable sequences, however we verify that only two sources are equivalents, the both physical. Therefore, we grouped the data from physical sources, and it became our groundtruth, then in sequence, we searched for trust regions. We adopted a non-parametric approach because we did not have no theoretical evidence about the distribution that follows the distance from the characteristic point to our groundtruth when a finite sequence of white noise candidate is analyzed. We then calculated the quantiles, respecting the factors sequence size (N), size of the word (D) and delay (¿), which serve as confidence regions for the test that gave rise to this work. We conclude the dissertation by verifying that sequences produced by community accepted generators generate characteristic points within confidence regions, while a generator that has been discarded by the structures that its sequences present leads to points outside these regions. We also applied the test to stationary and nonstationary sequences and, for the former, we make a preliminary assessment of the test power.