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Predicting future values of a random function

Peter, Hall and Tajvidi, Nader LU (2009) In Preprints in Mathematical Sciences1999-01-01+01:00 2009:4.
Abstract
Prediction from time-series data is traditionally accomplished using parametric, or at least structural, methods. For example, after removing trends, arguing that the time-series is an autoregression, and estimating the autoregressive parameters, we may predict future expected values, conditional on the past. In this paper, motivated by long meteorological maximum-temperature time-series, we suggest alternative approaches founded on functional data analysis. The new techniques make relatively few assumptions about the nature of the data, and allow consistent inference in cases where conventional models are inappropriate. They have both parametric and nonparametric forms. In the former context, our techniques are based on... (More)
Prediction from time-series data is traditionally accomplished using parametric, or at least structural, methods. For example, after removing trends, arguing that the time-series is an autoregression, and estimating the autoregressive parameters, we may predict future expected values, conditional on the past. In this paper, motivated by long meteorological maximum-temperature time-series, we suggest alternative approaches founded on functional data analysis. The new techniques make relatively few assumptions about the nature of the data, and allow consistent inference in cases where conventional models are inappropriate. They have both parametric and nonparametric forms. In the former context, our techniques are based on dimension-reduction and least-squares arguments; in the latter, they are founded on distance-based methods and statistical smoothing. We illustrate our method by application to Australian meteorological data, and by a simulation study designed to reflect those data. Theoretical arguments are used to demonstrate statistical consistency. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
unpublished
subject
keywords
statistical smoothing, parametric inference, prediction band, nonparametric inference, meteorology, kernel methods, functional data analysis, forecasting, Bootstrap, time series.
in
Preprints in Mathematical Sciences1999-01-01+01:00
volume
2009:4
pages
26 pages
publisher
Lund University
ISSN
1403-9338
language
English
LU publication?
yes
id
3d5352d6-8166-4373-beee-9c74f527b5b4 (old id 1701918)
date added to LUP
2011-12-29 17:46:55
date last changed
2017-02-08 13:49:27
@article{3d5352d6-8166-4373-beee-9c74f527b5b4,
  abstract     = {Prediction from time-series data is traditionally accomplished using parametric, or at least structural, methods. For example, after removing trends, arguing that the time-series is an autoregression, and estimating the autoregressive parameters, we may predict future expected values, conditional on the past. In this paper, motivated by long meteorological maximum-temperature time-series, we suggest alternative approaches founded on functional data analysis. The new techniques make relatively few assumptions about the nature of the data, and allow consistent inference in cases where conventional models are inappropriate. They have both parametric and nonparametric forms. In the former context, our techniques are based on dimension-reduction and least-squares arguments; in the latter, they are founded on distance-based methods and statistical smoothing. We illustrate our method by application to Australian meteorological data, and by a simulation study designed to reflect those data. Theoretical arguments are used to demonstrate statistical consistency.},
  author       = {Peter, Hall and Tajvidi, Nader},
  issn         = {1403-9338},
  keyword      = {statistical smoothing,parametric inference,prediction band,nonparametric inference,meteorology,kernel methods,functional data analysis,forecasting,Bootstrap,time series.},
  language     = {eng},
  pages        = {26},
  publisher    = {Lund University},
  series       = {Preprints in Mathematical Sciences1999-01-01+01:00},
  title        = {Predicting future values of a random function},
  volume       = {2009:4},
  year         = {2009},
}