Determining the order of the functional autoregressive model: ORDER OF FUNCTIONAL AUTOREGRESSION
提出一种多阶段检验程序来确定函数自回归过程FAR(p)的阶数p，利用函数主成分分析构建近似卡方分布的检验统计量，并通过模拟和信用卡交易、欧洲美元期货数据验证其有限样本性能。
We propose a multistage testing procedure to determine the order p of a functional autoregressive process, FAR (p). At its core is the representation of the FAR(p) process as a fully functional linear model with dependent regressors. Estimating the kernel function in this linear model allows us to construct a test statistic which has, approximately, a chi–square distribution with the number of degrees of freedom determined by the number of functional principal components used to represent the data. The asymptotic justification relies on the concept of Lp–m–approximability which quantifies the temporal dependence of functional time series. The procedure enjoys very good finite sample properties, as confirmed by a simulation study and applications to functional time series derived from credit card transactions and Eurodollar futures data.