A DATA-DRIVEN NONPARAMETRIC SPECIFICATION TEST FOR DYNAMIC REGRESSION MODELS
提出一种结合傅里叶级数回归的卡方统计量来检验动态回归模型的设定，通过数据驱动选择回归阶数，使检验在有限样本下尺寸准确且具有最优自适应速率。
The paper introduces a new nonparametric specification test for dynamic regression models. The test combines chi-square statistics based on Fourier series regression. A data-driven choice of the regression order, which uses the square root of the number of Fourier coefficients, is proposed. The benefits of the new test are (1) the selection procedure produces explicit and chi-square critical values that give a finite-sample size close to the nominal size; (2) the test is adaptive rate-optimal and detects local alternatives converging to the null with a rate that can be made arbitrarily close to the parametric rate. Simulation experiments illustrate the practical relevance of the new test.The first author acknowledges financial support from the Fonds Québécois de la Recherche sur la Société et la Culture (FQRSC). The second author acknowledges financial support from LSTA.