Multiscale decomposition and spectral analysis of sector ETF price dynamics

We present a multiscale analysis of the price dynamics of U.S. sector exchange-traded funds (ETFs). Our methodology features a multiscale noise-assisted approach, called the complementary ensemble empirical mode decomposition (CEEMD), that decomposes any financial time series into a number of intrinsic mode functions from high to low frequencies. By combining high-frequency modes or low-frequency modes, we show how to filter the financial time series and estimate conditional volatilities. The results show the different dynamics of the sector ETFs on multiple timescales. We then apply Hilbert spectral analysis to derive the instantaneous energy-frequency spectrum of each sector ETF. Using historical ETF prices, we illustrate and compare the properties of various timescales embedded in the original time series. Through the new metrics of the Hilbert power spectrum and frequency deviation, we are able to identify differences among sector ETF and with respect to SPY that were not obvious before.