Browsing by Subject "Multi-scaling"

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Open Access
Differentiating intraday seasonalities through wavelet multi-scaling
(Elsevier BV, 2001) Gençay, R.; Selçuk, F.; Whitcher, B.
It is well documented that strong intraday seasonalities may induce distortions in the estimation of volatility models. These seasonalities are also the dominant source for the underlying misspecifications 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.
Open Access
Scaling properties of foreign exchange volatility
(Elsevier BV, 2001) Gençay, R.; Selçuk, F.; Whitcher, B.
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.