Evidence of Nonlinearity in Daily Stock Returns
应用一种新统计技术，通过估计15只普通股日收益率时间序列的双谱，检验双谱偏度是否恒定，从而判断收益率生成过程是否为非线性。结果表明日股票收益率由非线性过程生成。
This article applies a newly developed statistical technique to time series of daily rates of return of 15 common stocks. The technique involves estimating the bispectrum of the observed time series. The bispectrum is defined as the double Fourier transform of the third-order cumulant function. If the process generating rates of return is linear with independent innovations, then the skewness of the bispectrum will be constant. The article describes a test that can detect nonconstant skewness in the bispectrum. Hence if the test rejects constant skewness, a nonlinear process is implied. As a consequence, the test can distinguish between white noise and purely random noise. The results suggest that daily stock returns are generated by a nonlinear process.