{'fraction_non_alphanumeric': 0.011872146118721462, 'fraction_numerical': 0.0036529680365296802, 'mean_word_length': 5.05524861878453, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
The Bootstrap for Testing the Equality of Two Multivariate Stochastic Processes with an Application to Financial Markets

: The problem of testing the equality of generating processes of two multivariate time series is addressed in this work. To this end, we construct two tests based on a distance measure between stochastic processes. The metric is deﬁned in terms of the quantile cross-spectral densities of both processes. A proper estimate of this dissimilarity is the cornerstone of the proposed tests. Both techniques are based on the bootstrap. Speciﬁcally, extensions of the moving block bootstrap and the stationary bootstrap are used for their construction. The approaches are assessed in a broad range of scenarios under the null and the alternative hypotheses. The results from the analyses show that the procedure based on the stationary bootstrap exhibits the best overall performance in terms of both size and power. The proposed techniques are used to answer the question regarding whether or not the dotcom bubble crash of the 2000s permanently impacted global market behavior.