Can The Wavelet-kernel Methodology Improve
Other Kernel Techniques?
Author(s)
M. Gago & E. Juaristi
Abstract
Our aim in this paper is to compare different ways of forecasting using the wavelet
transform and the kernel regression. We consider that working with block (or
segment) of data is richer than working with individual data (as in traditional
kernel), as we assume there is some kind of pattern inside each block which
will improve the estimation, and therefore the prediction. We choose the wavelet
transform because this transform is able to separate components of data in different
locations and with different location in time and frequency.To test the performance
of the different methodologies we have carried out a Monte Carlo Study in
which we have compared the four methodologies: Ordinary Least Square (OLS),
Traditional Kernel (TK), Block Kernel (BK) and Wavelet-Kernel (WK). Two real
life applications have been realized. On the one hand, volatility smile has been
forecast and on the other, the rated temperature of the steel coils’ furnace is
predicted. Surprisingly contradictory results had been obtained.
Keywords: wavelets, Kernel regression, bandwidth selection, implied volatility,
option pricing models, steel coils’ furnace’s rated temperature.
1 Introduction
The wavelet transform is a mathematical tool that is very used in several fields
such as engineering, mathematics, physics, economics or finance. It allows us to
separate data evolving in time in different frequency-time components. This way,
we will be able to identify in data its peaks and discontinuities using high scales
components and its long-trend or pattern using the low ones, because as it’s known
at low scales the wavelet transform has a large time support,whereas at high scales
has a small one.
Keywords
wavelets, Kernel regression, bandwidth selection, implied volatility,
option pricing models, steel coils’ furnace’s rated temperature.
Related Book
Other papers in this volume
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