Serial Correlation Robust LM

Jingjing Yang and Timothy Vogelsang

A chapter in 30th Anniversary Edition, 2012, pp 97-131 from Emerald Group Publishing Limited

Abstract: We analyze Lagrange Multiplier (LM) tests for a shift in trend of a univariate time series at an unknown date. We focus on the class of LM statistics based on nonparametric kernel estimates of the long run variance. Extending earlier work for models with nontrending data, we develop a fixed-b asymptotic theory for the statistics. The fixed-b theory suggests that, for a given statistic, kernel, and significance level, there usually exists a bandwidth such that the fixed-b asymptotic critical value is the same for both I(0) and I(1) errors. These “robust” bandwidths are calculated using simulation methods for a selection of well-known kernels. We find when the robust bandwidth is used, the supremum statistic configured with either the Bartlett or Daniell kernel gives LM tests with good power. When testing for a slope change, we obtain the surprising finding that less trimming of potential shift dates leads to higher power, which contrasts the usual relationship between trimming and power. Finite sample simulations indicate that the robust LM statistics have stable size with good power.

Keywords: Fixed-b asymptotics; structural change; long run variance; nonmonotonic power; kernel; robust bandwidth (search for similar items in EconPapers)
Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:eme:aecozz:s0731-9053(2012)0000030009

DOI: 10.1108/S0731-9053(2012)0000030009

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