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A Robust Test for Threshold‐Type Nonlinearity in Multivariate Time Series Analysis
Author(s) -
Chan WaiSum,
Cheung Siu Hung,
Chow Wai Kit,
Zhang LiXin
Publication year - 2015
Publication title -
journal of forecasting
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.543
H-Index - 59
eISSN - 1099-131X
pISSN - 0277-6693
DOI - 10.1002/for.2344
Subject(s) - univariate , outlier , autoregressive model , series (stratigraphy) , statistical hypothesis testing , test statistic , statistics , mathematics , nonlinear system , multivariate statistics , statistic , time series , econometrics , computer science , paleontology , physics , quantum mechanics , biology
There is growing interest in exploring potential forecast gains from the nonlinear structure of multivariate threshold autoregressive (MTAR) models. A least squares‐based statistical test has been proposed in the literature. However, previous studies on univariate time series analysis show that classical nonlinearity tests are often not robust to additive outliers. The outlier problem is expected to pose similar difficulties for multivariate nonlinearity tests. In this paper, we propose a new and robust MTAR‐type nonlinearity test, and derive the asymptotic null distribution of the test statistic. A Monte Carlo experiment is carried out to compare the power of the proposed test with that of the least squares‐based test under the influence of additive time series outliers. The results indicate that the proposed method is preferable to the classical test when observations are contaminated by outliers. Finally, we provide illustrative examples by applying the statistical tests to two real datasets. Copyright © 2015 John Wiley & Sons, Ltd.