Determining the order of the functional autoregressive model. (25th July 2012)

• Record Type: Journal Article
• Authors: Kokoszka, Piotr; Reimherr, Matthew
• Is Part Of: Journal of time series analysis. Volume 34:Number 1(2013:Jan.)
• Page Start: 116
• Page End: 129
• Publication Date: 2012-07-25
• Subjects: Time-series analysis -- Periodicals; 519.232
• DOI: 10.1111/j.1467-9892.2012.00816.x
• Languages: English
• ISSNs: 0143-9782

Abstract

<abstract abstract-type="main" xml:lang="en"> <title> <x xml:space="preserve">Abstract</x> </title> <p>We propose a multistage testing procedure to determine the order <italic>p</italic> of a functional autoregressive process, FAR (<italic>p</italic>). At its core is the representation of the FAR(<italic>p</italic>) 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 <italic>L</italic>^{<italic>p</italic>}–<italic>m</italic>–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.</p> </abstract>