Wavelet coefficient zeroing method for signal analysis and asset selection

Wavelet analysis has become a staple of signal analysis and processing across disciplines due to the compression and edge-detection qualities of the wavelet decomposition. The scaling and multi-resolution properties of the wavelet decomposition allows for time-scale analysis of time-series. This is an advantage over conventional Fourier methods due to large temporal support and the preservation of time-frequency details in non-stationary series. A wavelet coefficient zeroing method, to be explained in detail, allows for straightforward decimation of time-series at varying scale windows for determination of meaningful harmonic content. Elements of the S&P; 500 are an ideal subject for wavelet decimation of time-series, as daily pricing values of assets are outputs of a multi-scale process with a common index. Raw data of the S&P; 500 is readily available from Yahoo! Finance. A deterministic asset selection method utilizing wavelet analysis and Gaussian metrics is proposed. A wavelet decomposition of a single time-series with zeroing of successive levels of detail coefficients and subsequent reconstruction yields function-specific decimations of the original time-series over increasing time-frequency scales. Logarithmic and inverse logarithmic daily returns from closing prices are used to calculate Sharpe ratios of all S&P; 500 elements for each time-frequency scale subset. Sharpe ratios determine ranking and a theoretical investment portfolio is formed from the top ten assets of each subset. Numerous "blind period" bi-quarterly investment windows are provided to determine method efficacy. Raw returns are calculated for portfolios of each subset to gauge adherence of time-frequency decimation scales to Gaussian ranking metrics. Consistently higher returns are observed for portfolios within certain time-frequency scales specific to the wavelet functions utilized. Due to the computational intensity of processing calculations of hundreds of individual time-series, the use of a general-purpose graphics processing unit (GPGPU) is suggested to satisfy potential performance issues. A GPGPU implementation provides support of potential extensions of this method to real-world applications dealing with smaller time-scales and real-time feedback in a professional setting. Implementation of these research methods on GPGPU requires kernel support for wavelet decomposition and reconstruction methods, which is not investigated due to the prospective complexity of CUDA programming and the translation of wavelet functions to digital signal processing techniques. Simple batch processing gains are demonstrated for calculations of logarithmic daily returns, Sharpe ratio, and sorting procedures as per asset selection method on an nVidia Quadro 5000.