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This paper explores nonlinear cointegration between Chinese mainland stock markets and Hong Kong stock market in a multivariate framework for the period January, 1998 to December, 2014 by a nonparametric method. The local linear kernel smoothing method is developed to estimate the unknown function, and the practical problem of implementation is also addressed. Then, a simple nonparametric version of a bootstrap test is adapted for testing misspecification. Furthermore, Some Monte Carlo experiments are presented to examine the finite sample performance of the proposed procedure. Finally, the stock markets data set is discussed in detail by using proposed procedures, showing that Shanghai Stock Index (SHSI) and Shenzhen Component Index (SZCI) can affect Hang Seng Index (HSI), and the influence appears to be a strong nonlinear characteristics.

Semiparametric smoothing methods are usually used to model longitudinal data, and the interest is to improve efficiency for regression coefficients. This paper is concerned with the estimation in semiparametric varying-coefficient models (SVCMs) for longitudinal data. By the orthogonal projection method, local linear technique, quasiscore estimation, and quasi-maximum likelihood estimation, we propose a two-stage orthogonality-based method to estimate parameter vector, coefficient function vector, and covariance function. The developed procedures can be implemented separately and the resulting estimators do not affect each other. Under some mild conditions, asymptotic properties of the resulting estimators are established explicitly. In particular, the asymptotic behavior of the estimator of coefficient function vector at the boundaries is examined. Further, the finite sample performance of the proposed procedures is assessed by Monte Carlo simulation experiments. Finally, the proposed methodology is illustrated with an analysis of an acquired immune deficiency syndrome (AIDS) dataset. K E Y W O R D SAIDS data, asymptotic properties, local linear estimation, orthogonality, semiparametric varying coefficient models