BEGIN:VCALENDAR VERSION:2.0 PRODID:-//Talks.cam//talks.cam.ac.uk// X-WR-CALNAME:Talks.cam BEGIN:VEVENT SUMMARY:Testing for High-dimensional White Noise - Qiwei Yao (London Schoo l of Economics) DTSTART:20180201T110000Z DTEND:20180201T120000Z UID:TALK99490@talks.cam.ac.uk CONTACT:INI IT DESCRIPTION:Testing for white noise is a fundamental problem in stat istical inference\, as \;many testing problems in linear modelling can be transformed into a white \;noise test. While the celebrated Box-Pi erce test and its variants tests \;are often applied for model diagnos is\, their relevance in the context of \;high-dimensional modeling is not well understood\, as the asymptotic \;null distributions are estab lished for fixed dimensions. Furthermore\, \;those tests typically los e power when the dimension of time series is \;relatively large in rel ation to the sample size. In this talk\, we introduce \;two new omnibu s tests for high-dimensional time series.

The first method uses t he maximum absolute autocorrelations and \;cross-correlations of the c omponent series as the testing statistic. \;Based on an approximation by the L-infinity norm of a normal random \;vector\, the critical valu e of the test can be evaluated by bootstrapping \;from a multivariate normal distribution. In contrast to the conventional \;white noise tes t\, the new method is proved to be valid for testing \;departure from white noise that is not independent and identically \;distributed.

The second test statistic is defined as the sum of squared singular& nbsp\;values of the first q lagged sample autocovariance matrices. Therefo re\, it \;encapsulates all the serial correlations (up to the time lag q) within and \;across all component series. Using the tools from ran dom matrix theory\, \;we derive the normal limiting distributions when both the dimension and \;the sample size diverge to infinity.< br>


LOCATION:Seminar Room 2\, Newton Institute END:VEVENT END:VCALENDAR