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   -> Volume 9, Issue 5


Preprint: Two Papers on Multi-Scaling for Economics and Finance
 
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Brandon Whitcher (whitcher@eurandom.tue.nl)
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PostPosted: Wed Jun 07, 2000 11:51 pm    
Subject: Preprint: Two Papers on Multi-Scaling for Economics and Finance
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#6 Preprint: Two Papers on Multi-Scaling for Economics and Finance

Both papers are available for download at

http://www.eurandom.tue.nl/whitcher/papers/

Paper #1

"Differentiating Intraday Seasonalities Through Wavelet Multi-Scaling"

By R. Gencay, F. Selcuk and B. Whitcher

Abstract: It is well documented that strong intraday seasonalities may
induce distortions in the estimation of volatility models. These
periodicities are also the dominant source for the underlying
missspecifications of the various volatility models. Therefore, an
obvious route is to filter out the underlying intraday seasonalities
from the data.

In this paper, we propose a simple method for intraday seasonality
extraction that is free of model selection parameters which may affect
other intraday seasonality filtering methods. Our methodology is
based on a wavelet multi-scaling approach which decomposes the data
into its low and high frequency components through the application of
a non-decimated discrete wavelet transform. It is simple to calculate,
does not depend on a particular model selection criterion or model
specific parameter choices. The proposed filtering method is
translation invariant, has the ability to decompose an arbitrary
length series without boundary adjustments, is associated with a
zero-phase filter and is circular. Being circular helps to preserve
the entire sample unlike other two-sided filters where data loss
occurs from the beginning and the end of the studied sample.

--

Paper #2

"Multi-Scaling of Foreign Exchange Volatility"

By R. Gencay, F. Selcuk and B. Whitcher

Abstract: In this paper, we investigate the scaling properties of
foreign exchange volatility. Our methodology is based on a wavelet
multi-scaling approach which decomposes the variance of a time series
and the covariance between two time series on a scale by scale basis
through the application of a discrete wavelet transformation. It is
shown that foreign exchange rate volatilities follow different scaling
laws at different horizons. Particularly, there is a smaller degree of
persistence in intra-day volatility as compared to volatility at one
day and higher scales. Therefore, a common practice in the risk
management industry to convert risk measures calculated at shorter
horizons into longer horizons through a global scaling parameter may
not be appropriate.

This paper also demonstrates that correlation between the foreign
exchange volatilities is the lowest at the intra-day scales but
exhibits a gradual increase up to a daily scale. The correlation
coefficient stabilizes at scales one day and higher. Therefore, the
benefit of currency diversification is the greatest at the intra-day
scales and diminishes gradually at higher scales (lower
frequencies). The wavelet cross-correlation analysis also indicates
that the association between two volatilities is stronger at lower
frequencies.

--

Sincerely,

Brandon Whitcher

Until September 1, 2000: After September 1, 2000:
EURANDOM, P.O. Box 513 Geophysical Statistics Project
5600 MB Eindhoven NCAR, P.O. Box 3000
The Netherlands Boulder, CO 80307-3000
+31 40 247 8104 (voice)
+31 40 247 8190 (fax) (303) 497-1333 (fax)
whitcher@eurandom.tue.nl whitcher@ucar.edu
http://www.eurandom.tue.nl/whitcher/ http://www.cgd.ucar.edu/~whitcher/
All times are GMT + 1 Hour
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