关键词: 函数型数据分析, 部分函数型线性变系数模型, 序列相关检验, 经验似然

Abstract: Partially functional linear varying coefficient model (PFLVCM) was proposed in recent years as a new flexible model and gets widely used. In application, the economic and financial data collected often have serial correlation. Direct modeling without considering the correlation between the data will affect the accuracy and effectiveness of parameter estimation. This paper studies the serial correlation test for PFLVCM errors.Based on empirical likelihood, we extend the correlation test method for scalar time series data to functional data. And we propose the empirical log-likelihood ratio test statistic, and prove that our test statistic has an approximate distribution under the null hypothesis. Monte Carlo numerical simulation results show that the proposed test statistic has good performances in both size and power with finite sample size. Finally, the method is used to test whether the data of commercial electricity consumption in the United States has serial correlation,which proves the validity and practicability of the statistic.

Key words: Functional Data Analysis, Partially Functional Linear Varying Coefficient Model, Serial Correlation Test, Empirical Likelihood