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ROBUST TESTS FOR WHITE NOISE AND CROSS-CORRELATION

Published online by Cambridge University Press:  21 September 2020

Violetta Dalla
Affiliation:
National and Kapodistrian University of Athens
Liudas Giraitis*
Affiliation:
Queen Mary University of London
Peter C. B. Phillips
Affiliation:
Yale University, University of Auckland, University of Southampton, Singapore Management University
*
Address correspondence to Liudas Giraitis, Queen Mary University of London, London, UK; e-mail: l.giraitis@qmul.ac.uk.

Abstract

Commonly used tests to assess evidence for the absence of autocorrelation in a univariate time series or serial cross-correlation between time series rely on procedures whose validity holds for i.i.d. data. When the series are not i.i.d., the size of correlogram and cumulative Ljung–Box tests can be significantly distorted. This paper adapts standard correlogram and portmanteau tests to accommodate hidden dependence and nonstationarities involving heteroskedasticity, thereby uncoupling these tests from limiting assumptions that reduce their applicability in empirical work. To enhance the Ljung–Box test for non-i.i.d. data, a new cumulative test is introduced. Asymptotic size of these tests is unaffected by hidden dependence and heteroskedasticity in the series. Related extensions are provided for testing cross-correlation at various lags in bivariate time series. Tests for the i.i.d. property of a time series are also developed. An extensive Monte Carlo study confirms good performance in both size and power for the new tests. Applications to real data reveal that standard tests frequently produce spurious evidence of serial correlation.

Type
ARTICLES
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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Footnotes

Dalla acknowledges financial support from ELKE-EKPA. Phillips acknowledges support from the Kelly Fund at the University of Auckland, a KLC Fellowship at Singapore Management University, and the NSF under Grant No. SES 18-50860.

References

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