Wavelet Power: Wavelet Energy Ratio Unit Root Tests

Abstract

This paper uses wavelet theory to propose a frequency domain nonparametric and tuning parameter free family of unit root tests indexed by the fractional parameter d. The proposed test exploits the wavelet power spectrum of the observed series and its fractional partial sum to construct a test of the unit root based on the ratio of the resulting scaling energies. The construction takes its inspiration from the variance ratio (VR) unit root test of Nielsen (2009) and Fan and Gen cay (2010) (FG). The result is a statistic whose power properties virtually mimic that of the VR statistics but which drastically reduces the severe size distortions suffered by both the VR and FG test in the presence of serially correlated MA(1) errors when the MA parameter is close to negative unity. Any remaining size distortions are virtually eliminated using a modern wavelet resampling technique called wavestrapping. Finally, the test is visibly more robust to size distortions arising from lowering d than its VR counterpart and unlike the FG test, requires no estimation for construction.