A note on the estimation of functional autoregressive models
(English)Manuscript (Other academic)
Consider situations where a real valued function is observed over time and has a dynamic dependence structure. Linear autoregressive models, which have been proven useful to model dynamics of "pointwise" time series, can be generalized to such a functional time series situation. We call such models functional autoregressive models. Their parameters are functions of a real valued argument (as the data) and we consider a two-step estimation procedure inspired by Fan and Zhang's (2000) proposal for functional linear models. The latter proposal is based on a first step where the ordinary least squares is used to estimate pointwise linear models for given values of the argument of the functions observed. The second step smoothes the first-step estimates, regressing the latter on the mentioned arguments. The second step does not only yield smooth estimates of the functional parameters but also provides less variable pointwise estimates at the price of a bias. We do not only contribute by presenting an autoregressive model for functional data but also by proposing a two-stage estimator where the first step takes into account the contemporaneous correlation structure through a multivariate generalized least squares estimator. Some of the properties of the resulting two-step procedure are given. Financial functional data is used as an illustration.
Computer and Information Science
Research subject Econometrics
IdentifiersURN: urn:nbn:se:umu:diva-18756OAI: oai:DiVA.org:umu-18756DiVA: diva2:174705