Convolutional autoregressive models for functional time series

Xialu Liu; Han Xiao; Rong Chen

doi:https://doi.org/10.1016/j.jeconom.2016.05.006

Convolutional autoregressive models for functional time series

Xialu Liu, Han Xiao, Rong Chen

SAS - Statistics

Rutgers, The State University

Research output: Contribution to journal › Article › peer-review

12 Scopus citations

Abstract

Functional data analysis has became an increasingly popular class of problems in statistical research. However, functional data observed over time with serial dependence remains a less studied area. Motivated by Bosq (2000), who first introduced the functional autoregressive models, we propose a convolutional functional autoregressive model, where the function at time t is a result of the sum of convolutions of the past functions and a set of convolution functions, plus a noise process, mimicking the vector autoregressive process. It provides an intuitive and direct interpretation of the dynamics of a stochastic process. Instead of principal component analysis commonly used in functional data analysis, we adopt a sieve estimation procedure based on B-spline approximation of the convolution functions. We establish convergence rate of the proposed estimator, and investigate its theoretical properties. The model building, model validation, and prediction procedures are also developed. Both simulated and real data examples are presented.

Original language	English (US)
Pages (from-to)	263-282
Number of pages	20
Journal	Journal of Econometrics
Volume	194
Issue number	2
DOIs	https://doi.org/10.1016/j.jeconom.2016.05.006
State	Published - Oct 1 2016

ASJC Scopus subject areas

Economics and Econometrics

Keywords

Functional time series
Nonparametric methods
Sieve estimation
Spline methods

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title = "Convolutional autoregressive models for functional time series",

abstract = "Functional data analysis has became an increasingly popular class of problems in statistical research. However, functional data observed over time with serial dependence remains a less studied area. Motivated by Bosq (2000), who first introduced the functional autoregressive models, we propose a convolutional functional autoregressive model, where the function at time t is a result of the sum of convolutions of the past functions and a set of convolution functions, plus a noise process, mimicking the vector autoregressive process. It provides an intuitive and direct interpretation of the dynamics of a stochastic process. Instead of principal component analysis commonly used in functional data analysis, we adopt a sieve estimation procedure based on B-spline approximation of the convolution functions. We establish convergence rate of the proposed estimator, and investigate its theoretical properties. The model building, model validation, and prediction procedures are also developed. Both simulated and real data examples are presented.",

keywords = "Functional time series, Nonparametric methods, Sieve estimation, Spline methods",

author = "Xialu Liu and Han Xiao and Rong Chen",

note = "Funding Information: Xiao{\textquoteright}s research is partially supported by NSF grant DMS 1209091 . Chen{\textquoteright}s research is partially supported by NSF grants DMS 1209085 and DMS 1513409 . We would like to thank the editor and two anonymous referees for their valuable comments and suggestions which led to a substantial improvement of the paper. Publisher Copyright: {\textcopyright} 2016 Elsevier B.V.",

year = "2016",

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AU - Liu, Xialu

AU - Xiao, Han

AU - Chen, Rong

N1 - Funding Information: Xiao’s research is partially supported by NSF grant DMS 1209091 . Chen’s research is partially supported by NSF grants DMS 1209085 and DMS 1513409 . We would like to thank the editor and two anonymous referees for their valuable comments and suggestions which led to a substantial improvement of the paper. Publisher Copyright: © 2016 Elsevier B.V.

PY - 2016/10/1

Y1 - 2016/10/1

N2 - Functional data analysis has became an increasingly popular class of problems in statistical research. However, functional data observed over time with serial dependence remains a less studied area. Motivated by Bosq (2000), who first introduced the functional autoregressive models, we propose a convolutional functional autoregressive model, where the function at time t is a result of the sum of convolutions of the past functions and a set of convolution functions, plus a noise process, mimicking the vector autoregressive process. It provides an intuitive and direct interpretation of the dynamics of a stochastic process. Instead of principal component analysis commonly used in functional data analysis, we adopt a sieve estimation procedure based on B-spline approximation of the convolution functions. We establish convergence rate of the proposed estimator, and investigate its theoretical properties. The model building, model validation, and prediction procedures are also developed. Both simulated and real data examples are presented.

AB - Functional data analysis has became an increasingly popular class of problems in statistical research. However, functional data observed over time with serial dependence remains a less studied area. Motivated by Bosq (2000), who first introduced the functional autoregressive models, we propose a convolutional functional autoregressive model, where the function at time t is a result of the sum of convolutions of the past functions and a set of convolution functions, plus a noise process, mimicking the vector autoregressive process. It provides an intuitive and direct interpretation of the dynamics of a stochastic process. Instead of principal component analysis commonly used in functional data analysis, we adopt a sieve estimation procedure based on B-spline approximation of the convolution functions. We establish convergence rate of the proposed estimator, and investigate its theoretical properties. The model building, model validation, and prediction procedures are also developed. Both simulated and real data examples are presented.

KW - Functional time series

KW - Nonparametric methods

KW - Sieve estimation

KW - Spline methods

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ER -

Convolutional autoregressive models for functional time series

Abstract

ASJC Scopus subject areas

Keywords

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