{'fraction_non_alphanumeric': 0.017873941674506115, 'fraction_numerical': 0.0, 'mean_word_length': 5.52760736196319, '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}}
BAYESIAN ESTIMATION OF COMMON LONG-RANGE DEPENDENT MODELS

We present a sampling-based Bayesian approach for modeling and forecasting a bivariate process having a long-range dependent component that is common to each series and additive short-range dependent noise terms that are unique to each series. A common long-range dependent component might be observed, for instance, in two climatological series collected in the same geographic region. We use an ARMA model to approximate the common long-range dependent behavior in a Gibbs sampling framework and then use importance sampling to adjust for the approximation. The sampling-based approach is computationally more feasible than methods that depend on exact evaluation of the likelihood function and gives comparable results. Additionally, complete posterior distributions for the estimated parameters, longand short-range dependent component series, and future series values can be obtained. We illustrate the technique using two wind speed series collected at different meteorological stations in Ireland.