In this article, a semiparametric time‐varying nonlinear vector autoregressive (NVAR) model is proposed to model nonlinear vector time series data. We consider a combination of parametric and nonparametric estimation approaches to estimate the NVAR function for both independent and dependent errors. We use the multivariate Taylor series expansion of the link function up to the second order which has a parametric framework as a representation of the nonlinear vector regression function. After the unknown parameters are estimated by the maximum likelihood estimation procedure, the obtained NVAR function is adjusted by a nonparametric diagonal matrix, where the proposed adjusted matrix is estimated by the nonparametric kernel estimator. The asymptotic consistency properties of the proposed estimators are established. Simulation studies are conducted to evaluate the performance of the proposed semiparametric method. A real data example on short‐run interest rates and long‐run interest rates of United States Treasury securities is analyzed to demonstrate the application of the proposed approach. The Canadian Journal of Statistics 47: 668–687; 2019 © 2019 Statistical Society of Canada

中文翻译：

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建模非线性非线性时间序列的半参数方法

本文提出了一种半参数时变非线性向量自回归（NVAR）模型来对非线性向量时间序列数据进行建模。我们考虑参数和非参数估计方法的组合，以针对独立和相关误差估计NVAR函数。我们使用链接函数的多元泰勒级数展开式直到第二阶，该展开式具有参数框架作为非线性矢量回归函数的表示。在通过最大似然估计程序估计未知参数之后，通过非参数对角矩阵对获得的NVAR函数进行调整，其中建议的调整矩阵由非参数核估计器进行估计。建立了所提出估计量的渐近一致性性质。仿真研究进行了评估所提出的半参数方法的性能。分析了有关美国国库券短期利率和长期利率的真实数据示例，以证明该方法的应用。加拿大统计杂志47：668-687；加拿大统计杂志。2019©2019加拿大统计学会