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Determining the order of the functional autoregressive model
Author(s) -
Kokoszka Piotr,
Reimherr Matthew
Publication year - 2013
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/j.1467-9892.2012.00816.x
Subject(s) - autoregressive model , mathematics , functional principal component analysis , functional data analysis , test statistic , series (stratigraphy) , representation (politics) , econometrics , statistics , statistical hypothesis testing , paleontology , politics , political science , law , biology
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 L p – 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.