We propose a Cram\'{e}r-von Mises (CM) statistics for diagnostic checking of weak vector autoregressive models, where the errors are assumed to be uncorrelated but not necessarily independent. The test statistics is constructed based on the distance between the sample periodogram of the residuals and a constant. Unlike portmanteau tests in the time domain that utilize only the first $m$ lags autocorrelations of the residuals, our spectral test effectively detect correlations beyond m lags. We study the asymptotic properties of the test statistics, noting that the dependent structure of the errors and estimation uncertainty render the test non-asymptotically pivotal. To address this, we employ a (blockwise) random weighting bootstrap method to approximate the critical values, thereby justifying its validity. The finite sample performance of the testing procedure is demonstrated through extensive Monte Carlo simulations, along with a real data application.
嘉宾介绍
李木易，香港大学统计学博士，现任厦门大学 WISE 与经济学院统计学与数据科学系双聘教授、博士生导师、系副主任。主要研究方向为非线性时间序列、金融计量、模型检验、时间序列预测等。论文发表于Journal of Econometrics, Journal of Business and Economic Statistics，Journal of Time Series Analysis, International Journal of Forecasting等国际权威期刊。主持国家自然科学基金3项、全国统计科学研究重点项目1项，以及福建省社科规划项目、福建省自科基金项目、教育部计量经济学重点实验室实验教学项目等。参与国家自然科学基金重点项目“经济大数据的宏观计量建模: 理论、方法和应用”。主讲中国大学慕课《时间序列分析》。
