{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,20]],"date-time":"2026-09-20T13:47:57Z","timestamp":1789912077944,"version":"4.0.1"},"reference-count":47,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2010,8,27]],"date-time":"2010-08-27T00:00:00Z","timestamp":1282867200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Econom. Theory"],"published-print":{"date-parts":[[2011,4]]},"abstract":"<jats:p>Testing for white noise has been well studied in the literature of econometrics and statistics. For most of the proposed test statistics, such as the well-known Box\u2013Pierce test statistic with fixed lag truncation number, the asymptotic null distributions are obtained under independent and identically distributed assumptions and may not be valid for dependent white noise. Because of recent popularity of conditional heteroskedastic models (e.g., generalized autoregressive conditional heteroskedastic [GARCH] models), which imply nonlinear dependence with zero autocorrelation, there is a need to understand the asymptotic properties of the existing test statistics under unknown dependence. In this paper, we show that the asymptotic null distribution of the Box\u2013Pierce test statistic with general weights still holds under unknown weak dependence as long as the lag truncation number grows at an appropriate rate with increasing sample size. Further applications to diagnostic checking of the autoregressive moving average (ARMA) and fractional autoregressive integrated moving average (FARIMA) models with dependent white noise errors are also addressed. Our results go beyond earlier ones by allowing non-Gaussian and conditional heteroskedastic errors in the ARMA and FARIMA models and provide theoretical support for some empirical findings reported in the literature.<\/jats:p>","DOI":"10.1017\/s0266466610000253","type":"journal-article","created":{"date-parts":[[2010,8,27]],"date-time":"2010-08-27T12:49:26Z","timestamp":1282913366000},"page":"312-343","source":"Crossref","is-referenced-by-count":45,"title":["TESTING FOR WHITE NOISE UNDER UNKNOWN DEPENDENCE AND ITS APPLICATIONS TO DIAGNOSTIC CHECKING FOR TIME SERIES MODELS"],"prefix":"10.1017","volume":"27","author":[{"given":"Xiaofeng","family":"Shao","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2010,8,27]]},"reference":[{"key":"S0266466610000253_ref20","doi-asserted-by":"crossref","DOI":"10.1063\/1.3060405","volume-title":"Statistical Analysis of Stationary Time Series","author":"Grenander","year":"1957"},{"key":"S0266466610000253_ref22","volume-title":"Martingale Limit Theory and Its Applications","author":"Hall","year":"1980"},{"key":"S0266466610000253_ref31","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/asn014"},{"key":"S0266466610000253_ref11","doi-asserted-by":"publisher","DOI":"10.1214\/009053605000000606"},{"key":"S0266466610000253_ref10","doi-asserted-by":"publisher","DOI":"10.1111\/1467-9892.00162"},{"key":"S0266466610000253_ref29","doi-asserted-by":"publisher","DOI":"10.1214\/009117904000000333"},{"key":"S0266466610000253_ref38","doi-asserted-by":"publisher","DOI":"10.1214\/009053605000000354"},{"key":"S0266466610000253_ref5","doi-asserted-by":"crossref","first-page":"919","DOI":"10.1214\/aos\/1013699986","article-title":"Least absolute deviation estimation for all-pass time series models","volume":"29","author":"Breidt","year":"2001","journal-title":"Annals of Statistics"},{"key":"S0266466610000253_ref3","doi-asserted-by":"crossref","first-page":"659","DOI":"10.1111\/j.2517-6161.1995.tb02054.x","article-title":"Maximum likelihood estimation of the differencing parameter for invertible short and long memory autoregressive integrated moving average models","volume":"57","author":"Beran","year":"1995","journal-title":"Journal of the Royal Statistical Society, Series B"},{"key":"S0266466610000253_ref4","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1970.10481180"},{"key":"S0266466610000253_ref2","doi-asserted-by":"crossref","first-page":"749","DOI":"10.1111\/j.2517-6161.1992.tb01448.x","article-title":"A goodness-of-fit test for time series with long range dependence","volume":"54","author":"Beran","year":"1992","journal-title":"Journal of the Royal Statistical Society, Series B"},{"key":"S0266466610000253_ref15","doi-asserted-by":"publisher","DOI":"10.1198\/016214504000001510"},{"key":"S0266466610000253_ref9","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466606060099"},{"key":"S0266466610000253_ref16","doi-asserted-by":"publisher","DOI":"10.1016\/S0378-3758(99)00109-3"},{"key":"S0266466610000253_ref14","doi-asserted-by":"publisher","DOI":"10.5194\/nhess-4-277-2004"},{"key":"S0266466610000253_ref17","doi-asserted-by":"publisher","DOI":"10.1007\/0-387-24555-3_12"},{"key":"S0266466610000253_ref13","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4076(91)90025-9"},{"key":"S0266466610000253_ref12","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-4076(00)00027-0"},{"key":"S0266466610000253_ref18","volume-title":"An Introduction to Bilinear Time Series Models","author":"Granger","year":"1978"},{"key":"S0266466610000253_ref23","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2005.06.015"},{"key":"S0266466610000253_ref37","volume-title":"Spectral Analysis and Time Series","volume":"1","author":"Priestley","year":"1981"},{"key":"S0266466610000253_ref39","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1996.10476928"},{"key":"S0266466610000253_ref43","doi-asserted-by":"publisher","DOI":"10.1214\/009117907000000060"},{"key":"S0266466610000253_ref26","doi-asserted-by":"publisher","DOI":"10.1016\/j.jeconom.2005.06.014"},{"key":"S0266466610000253_ref21","doi-asserted-by":"publisher","DOI":"10.1214\/009053604000001200"},{"key":"S0266466610000253_ref33","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1997.10474076"},{"key":"S0266466610000253_ref42","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.0506715102"},{"key":"S0266466610000253_ref8","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9868.2004.00435.x"},{"key":"S0266466610000253_ref7","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466604202067"},{"key":"S0266466610000253_ref6","volume-title":"Time Series: Data Analysis and Theory","author":"Brillinger","year":"1975"},{"key":"S0266466610000253_ref24","doi-asserted-by":"publisher","DOI":"10.2307\/2171847"},{"key":"S0266466610000253_ref25","unstructured":"Hong Y. & Lee Y.J. 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