Wavelet power spectrum analysis of ETF’s tracking error

Abstract

PurposeThis study examines the tracking error (TE) of a sample of sector exchange traded funds (ETFs) using spectral techniques.Design/methodology/approachTE is examined by computing its power spectrum using the wavelet transform. The wavelet transform maps the TE time series from the time domain to the time–frequency domain. Albeit the wavelet transform is a more complicated mathematical tool compared with the Fourier transform, it also has important advantages such as that it allows to analyze non-stationary data and to detect transient behavior.FindingsResults show that changes in the TE of a sample of sector ETFs are captured by the wavelet transform. Moreover, the authors also find that the wavelet coherence function can be used as a measure of TE in the time–frequency domain.Originality/valueThe study shows that the wavelet coherence function can be used as a reliable measure of TE.