{'fraction_non_alphanumeric': 0.024752475247524754, 'fraction_numerical': 0.006600660066006601, 'mean_word_length': 5.00990099009901, '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}}
A joint test of fractional cyclic integration and a linear time trend

We propose in this article a joint test for testing simultaneously a deterministic trend component and the degree of integration of the cyclical component in a given time series. The test is directly derived from Robinson's (1994) procedure, which is based on the Lagrange Multiplier (LM) principle. Thus, it has standard null and local asymptotic distributions. However, finite-sample critical values of the tests are evaluated and, an empirical application using historical annual data, is also carried out at the end of the article.