Denoising Non-stationary Signals by Dynamic Multivariate Complex Wavelet Thresholding

Abstract

Over the past few years, we have seen an increased need for analyzing the dynamically changing behaviors of economic and financial time series. These needs have led to significant demand for methods that denoise non-stationary time series across time and for specific investment horizons (scales) and localized windows (blocks) of time. Wavelets have long been known to decompose non-stationary time series into their different components or scale pieces. Recent methods satisfying this demand first decompose the non-stationary time series using wavelet techniques and then apply a thresholding method to separate and capture the signal and noise components of the series. Traditionally, wavelet thresholding methods rely on the discrete wavelet transforms (DWT), a static thresholding technique that may not capture the time series of the estimated variance in the additive noise process. We introduce a novel continuous wavelet transform (CWT) dynamically-optimized, multivariate thresholding method. Applying this method we are simultaneously able to separate and capture the signal and noise components while estimating the dynamic noise variance. Our method shows improved results when compared to well-known methods, especially for high-frequency signal rich time series, typically observed in finance. Supplementary materials for your article are available online.

Keywords: Continuous wavelet transform, data-driven and adaptive thresholding, partial density estimation, integrated squared error, WaveL2E, nonparametric method

JEL Classification: C14, C15, C02, C00, C13