Differentiating intraday seasonalities through wavelet multi-scaling

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.