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The test statistic is a normalized weighted maximum sample correlation coefficient <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0266466619000367_inline1.png\"\/><jats:tex-math>$ \\max _{1\\leq h\\leq \\mathcal {L}_{n}}\\sqrt {n}|\\hat {\\omega }_{n}(h)\\hat {\\rho }_{n}(h)|$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>, where <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0266466619000367_inline2.png\"\/><jats:tex-math>$\\hat {\\omega }_{n}(h)$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> are weights and the maximum lag <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0266466619000367_inline3.png\"\/><jats:tex-math>$ \\mathcal {L}_{n}$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> increases at a rate slower than the sample size <jats:italic>n<\/jats:italic>. We only require uncorrelatedness under the null hypothesis, along with a moment contraction dependence property that includes mixing and nonmixing sequences. We show Shao\u2019s (2011, <jats:italic>Annals of Statistics<\/jats:italic> 35, 1773\u20131801) dependent wild bootstrap is valid for a much larger class of processes than originally considered. It is also valid for residuals from a general class of parametric models as long as the bootstrap is applied to a first-order expansion of the sample correlation. We prove the bootstrap is asymptotically valid without exploiting extreme value theory (standard in the literature) or recent Gaussian approximation theory. Finally, we extend Escanciano and Lobato\u2019s (2009, <jats:italic>Journal of Econometrics<\/jats:italic> 151, 140\u2013149) automatic maximum lag selection to our setting with an unbounded lag set that ensures a consistent white noise test, and find it works extremely well in controlled experiments.<\/jats:p>","DOI":"10.1017\/s0266466619000367","type":"journal-article","created":{"date-parts":[[2020,5,12]],"date-time":"2020-05-12T05:35:02Z","timestamp":1589261702000},"page":"907-960","source":"Crossref","is-referenced-by-count":12,"title":["A MAX-CORRELATION WHITE NOISE TEST FOR WEAKLY DEPENDENT TIME SERIES"],"prefix":"10.1017","volume":"36","author":[{"given":"Jonathan B.","family":"Hill","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kaiji","family":"Motegi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2020,5,12]]},"reference":[{"key":"S0266466619000367_r61","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466600005296"},{"key":"S0266466619000367_r21","doi-asserted-by":"publisher","DOI":"10.1198\/jasa.2011.tm10226"},{"key":"S0266466619000367_r18","doi-asserted-by":"publisher","DOI":"10.1093\/0198774036.001.0001"},{"key":"S0266466619000367_r38","article-title":"Convergence of stochastic processes on Polish spaces","author":"Hoffmann-J\u00f8rgensen","year":"1991","journal-title":"Various Publications Series 39"},{"key":"S0266466619000367_r41","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2005.06.014"},{"key":"S0266466619000367_r8","doi-asserted-by":"publisher","DOI":"10.1112\/jlms\/s2-8.2.339"},{"key":"S0266466619000367_r70","doi-asserted-by":"publisher","DOI":"10.2307\/1913828"},{"key":"S0266466619000367_r24","doi-asserted-by":"publisher","DOI":"10.1214\/aop\/1176995384"},{"key":"S0266466619000367_r66","first-page":"2","article-title":"Empirical processes: Theory and applications","author":"Pollard","year":"1990","journal-title":"NSF-CBMS Regional Conference Series in Probability and Statistics"},{"key":"S0266466619000367_r60","doi-asserted-by":"publisher","DOI":"10.1111\/j.1368-423X.2012.00379.x"},{"key":"S0266466619000367_r29","doi-asserted-by":"publisher","DOI":"10.1002\/9780470670057"},{"key":"S0266466619000367_r56","doi-asserted-by":"publisher","DOI":"10.1214\/aop\/1176996269"},{"key":"S0266466619000367_r54","doi-asserted-by":"publisher","DOI":"10.1198\/016214501753208726"},{"key":"S0266466619000367_r7","doi-asserted-by":"publisher","DOI":"10.1002\/9780470316962"},{"key":"S0266466619000367_r75","first-page":"246","article-title":"A disproof of a conjecture of Erd\u00f6s in Ramsey theory","volume":"39","author":"Thomason","year":"1988","journal-title":"Journal of the London Mathematical Society"},{"key":"S0266466619000367_r26","doi-asserted-by":"publisher","DOI":"10.1007\/BF00534202"},{"key":"S0266466619000367_r4","doi-asserted-by":"publisher","DOI":"10.1007\/BF02213360"},{"key":"S0266466619000367_r77","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.0506715102"},{"key":"S0266466619000367_r48","unstructured":"Le Cam, L. 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