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A FIXED‐ b TEST FOR A BREAK IN LEVEL AT AN UNKNOWN TIME UNDER FRACTIONAL INTEGRATION
Author(s) -
Iacone Fabrizio,
Leybourne Stephen J.,
Robert Taylor A. M.
Publication year - 2014
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/jtsa.12049
Subject(s) - mathematics , wald test , autocorrelation , estimator , asymptotic distribution , statistic , series (stratigraphy) , statistics , test statistic , parametric statistics , statistical hypothesis testing , limit (mathematics) , likelihood ratio test , mathematical analysis , paleontology , biology
In this paper, we propose a test for a break in the level of a fractionally integrated process when the timing of the putative break is not known. This testing problem has received considerable attention in the literature in the case where the time series is weakly autocorrelated. Less attention has been given to the case where the underlying time series is allowed to be fractionally integrated. Here, valid testing can only be performed if the limiting null distribution of the level break test statistic is well defined for all values of the fractional integration exponent considered. However, conventional sup‐Wald type tests diverge when the data are strongly autocorrelated. We show that a sup‐Wald statistic, which is standardized using a non‐parametric kernel‐based long‐run variance estimator, does possess a well‐defined limit distribution, depending only on the fractional integration parameter, provided the recently developed fixed‐ b asymptotic framework is applied. We give the appropriate asymptotic critical values for this sup‐Wald statistic and show that it has good finite sample size and power properties.