TY - JOUR
T1 - Martingale decomposition and approximations for nonlinearly dependent processes
AU - Lee, JiHyung
N1 - Publisher Copyright:
© 2019 Elsevier B.V.
Copyright:
Copyright 2019 Elsevier B.V., All rights reserved.
PY - 2019/9
Y1 - 2019/9
N2 - This paper proposes a new martingale (MG) decomposition (Gordin, 1969; Hall and Heyde, 1980) for a dependent time series under a predictive dependence measure based on Wu (2005). The decomposition produces a generalized version of the Beveridge–Nelson (BN) lemma (Phillips and Solo, 1992) that accommodates many nonlinear time series, such as GARCH models and threshold autoregressive processes, thereby extending the empirical ambit of the original lemma designed for the linear process. Under this extended framework, MG approximations can be constructed for weighted sums of the nonlinear dependent processes and these approximations lead directly to a new central limit theorem whose range of application includes many practical time series models.
AB - This paper proposes a new martingale (MG) decomposition (Gordin, 1969; Hall and Heyde, 1980) for a dependent time series under a predictive dependence measure based on Wu (2005). The decomposition produces a generalized version of the Beveridge–Nelson (BN) lemma (Phillips and Solo, 1992) that accommodates many nonlinear time series, such as GARCH models and threshold autoregressive processes, thereby extending the empirical ambit of the original lemma designed for the linear process. Under this extended framework, MG approximations can be constructed for weighted sums of the nonlinear dependent processes and these approximations lead directly to a new central limit theorem whose range of application includes many practical time series models.
KW - Dependence
KW - Martingale approximations
KW - Nonlinear time series
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U2 - 10.1016/j.spl.2019.04.012
DO - 10.1016/j.spl.2019.04.012
M3 - Article
SN - 0167-7152
VL - 152
SP - 35
EP - 42
JO - Statistics and Probability Letters
JF - Statistics and Probability Letters
ER -