Predicting future values of a random function
(2009) In Preprints in Mathematical Sciences 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)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/1701918
- author
- Peter, Hall
and Tajvidi, Nader
LU
- organization
- publishing date
- 2009
- 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- unpublished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 Sciences
- 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
- 2016-04-01 14:28:30
- date last changed
- 2018-11-21 20:27:06
@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}}, keywords = {{statistical smoothing; parametric inference; prediction band; nonparametric inference; meteorology; kernel methods; functional data analysis; forecasting; Bootstrap; time series.}}, language = {{eng}}, publisher = {{Lund University}}, series = {{Preprints in Mathematical Sciences}}, title = {{Predicting future values of a random function}}, volume = {{2009:4}}, year = {{2009}}, }