Abstract:

When one applies the wavelet transform to analyze finite-length time series, discontinuities at the data boundaries will distort its wavelet power spectrum in some regions which are defined as a wavelength- dependent cone of influence (COI). In the COI, significance tests are unreliable. At the same time, as many time series are short and noisy, the COI is a serious limitation in wavelet analysis of time series. In this paper, we will give a method to reduce boundary effects and discover significant frequencies in the COI. After that, we will apply our method to analyze Greenland winter temperature and Baltic sea ice. The new method makes use of line removal and odd extension of the time series. This causes the derivative of the series to be continuous (unlike the case for other padding methods). This will give the most reasonable padding methodology if the time series being analyzed has red noise characteristics.

Key words: wavelet power spectrum, significance testing, Greenland winter temperature, Baltic sea ice