Narrow Results

It is widely believed that implied volatilities contains information that would enable prediction of spot volatility for a wide range of financial assets. Lead-lag analysis based on the Discrete Wavelet Transform has been proposed as one method for identifying and extracting that predictive information. Unfortunately this approach can fail to identify periodic components that are not proportional to an increasing dyadic scale. We propose a multiscale analysis of the Eurodollar realized volatility and at-the-money (ATM) implied volatilities. After filtering the long memory components we produce a decomposition of cross-correlation by using wavelet packet methods. A threshold cost functional based on asymptotic confidence intervals was used along with the best basis algorithm in order to select an adaptive frequency partition of the sample cross-correlation. We found substantial evidence that Eurodollar implied volatilities contain predictive information about realized volatilities. Moreover, in our analysis the new technique outperforms the lead-lag analysis based on the nondecimated Discrete Wavelet Transform. Therefore we contend that the proposed technique will improve detection of predictive information and recommend further testing in a range of applied contexts.

In this study, in order to verify the effectiveness of the variable filter band discrete wavelet transform (VFB-DWT) and construction method of the variable-band filter (VBF), a fetal ECG extraction has been carried out and the main results obtained are as follows. The approach to configuration VBF by selecting the frequency band only where the fetal ECG component is present was effective to configure the optimal base sensible signal. The extraction of the fetal ECG was successful by applying the wavelet shrinkage to VFB-DWT, which used the constructed VBF. The information entropy was selected as an evaluation index, and two kinds of ECG signals are used to evaluate the wavelet transform basis between the wavelet packet transform (WPT) and the VFB-DWT. One is a synthesized signal composed of white noise, the maternal ECG and the fetal ECG. The other signal is the real target signal separated by independent component analysis (ICA) and has the mother's body noise, the maternal ECG and the fetal ECG. The result shows that the basis by VBF of the VFB-DWT is better than the basis of the WPT that was chosen by the best basis algorithm (BBA).