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Abstract Details

Activity Number: 285
Type: Topic Contributed
Date/Time: Tuesday, July 31, 2012 : 8:30 AM to 10:20 AM
Sponsor: Section on Statistical Learning and Data Mining
Abstract - #304159
Title: Testing for White Noise Against Locally Stationary Alternatives
Author(s): Georg Matthias Goerg*+
Companies: Carnegie Mellon University
Address: , Pittsburgh, PA, 15213,
Keywords: autocorrelations ; Ljung-Box ; white noise ; locally stationary ; residual check ; time varying

Many real-world systems have dynamics that evolve over time, yet stationary models still remain a popular choice in empirical time series studies. In this work I show that one reason for seemingly correct stationary models is a very low power of classic white noise tests against locally varying dynamics. In particular, if autocorrelations change over time but on average equal zero, standard white noise tests cannot detect this deviation from the null hypothesis due to their fundamental design. Here I introduce a moving-window version of the Ljung-Box statistic with an asymptotic chi-square distribution under the null and much larger power facing processes with time-varying autocorrelations. Simulations also show that stationary models often provide a spuriously good fit and thus time-varying dynamics remain undetected in the first place. A case study of tree-ring data demonstrates the importance of the new test for applied time series studies.

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