TEST (2017) 26:574–599
Jump-detection-based estimation in time-varying
coefﬁcient models and empirical applications
· Jin-Guan Lin
· Hong-Xia Wang
Received: 9 May 2016 / Accepted: 20 January 2017 / Published online: 10 February 2017
© Sociedad de Estadística e Investigación Operativa 2017
Abstract Time-varying coefﬁcient models are very important tools to explore the hid-
den structure between the response variable and its predictors. In some applications, the
coefﬁcient curveshave singularities, including jump points at some unknown positions,
representing structural changes of the related processes. Detection of such singulari-
ties is important for understanding the structural changes. In this paper, an alternative
jump-detection procedure is proposed based on the ﬁrst-order and second-order deriva-
tives of the coefﬁcient curves. Based on the detected jump points, a coefﬁcient curve
estimation procedure is also proposed, which can preserve the jump structure well
when the noise level is small. Further, the implementation of turning parameters is
discussed. Under some mild conditions, the asymptotic properties of the proposed
estimators are established not only in the continuous regions of coefﬁcient functions,
but also in the neighborhoods of the jump points. Finally, we demonstrate, using both
simulation and empirical examples, that the proposed methodologies perform well.
Keywords Bootstrap · Local polynomial estimation · Jump detection · Turning
parameters · Time-varying coefﬁcient
The research work is supported by the National Natural Science Foundation of China under Grant Nos.
11571073, 11501099, the Natural Science Foundation of Jiangsu Province of China under Grant Nos.
BK20141326, BK20140617 and the Priority Academic Program Development of Jiangsu Higher
Electronic supplementary material The online version of this article (doi:10.1007/s11749-017-0525-7)
contains supplementary material, which is available to authorized users.
Department of Statistics, Nanjing Audit University, Nanjing 211815, People’s Republic of China