TY - THES

T1 - Modelling nonlinear time series using selection methods and information criteria

AU - Nakamura, Tomomichi

PY - 2003

Y1 - 2003

N2 - [Truncated abstract] Time series of natural phenomena usually show irregular fluctuations. Often we want to know the underlying system and to predict future phenomena. An effective way of tackling this task is by time series modelling. Originally, linear time series models were used. As it became apparent that nonlinear systems abound in nature, modelling techniques that take into account nonlinearity in time series were developed. A particularly convenient and general class of nonlinear models is the pseudolinear models, which are linear combinations of nonlinear functions. These models can be obtained by starting with a large dictionary of basis functions which one hopes will be able to describe any likely nonlinearity, selecting a small subset of it, and taking a linear combination of these to form the model. The major component of this thesis concerns how to build good models for nonlinear time series. In building such models, there are three important problems, broadly speaking. The first is how to select basis functions which reflect the peculiarities of the time series as much as possible. The second is how to fix the model size so that the models can reflect the underlying system of the data and the influences of noise included in the data are removed as much as possible. The third is how to provide good estimates for the parameters in the basis functions, considering that they may have significant bias when the noise included in the time series is significant relative to the nonlinearity. Although these problems are mentioned separately, they are strongly interconnected

AB - [Truncated abstract] Time series of natural phenomena usually show irregular fluctuations. Often we want to know the underlying system and to predict future phenomena. An effective way of tackling this task is by time series modelling. Originally, linear time series models were used. As it became apparent that nonlinear systems abound in nature, modelling techniques that take into account nonlinearity in time series were developed. A particularly convenient and general class of nonlinear models is the pseudolinear models, which are linear combinations of nonlinear functions. These models can be obtained by starting with a large dictionary of basis functions which one hopes will be able to describe any likely nonlinearity, selecting a small subset of it, and taking a linear combination of these to form the model. The major component of this thesis concerns how to build good models for nonlinear time series. In building such models, there are three important problems, broadly speaking. The first is how to select basis functions which reflect the peculiarities of the time series as much as possible. The second is how to fix the model size so that the models can reflect the underlying system of the data and the influences of noise included in the data are removed as much as possible. The third is how to provide good estimates for the parameters in the basis functions, considering that they may have significant bias when the noise included in the time series is significant relative to the nonlinearity. Although these problems are mentioned separately, they are strongly interconnected

KW - Time-series analysis

KW - Mathematical models

KW - Nonlinear time series

KW - Parameter estimation

KW - Selection methods

M3 - Doctoral Thesis

ER -