Using the correlation exponent to decide whether an economic series is chaotic
比较了Grassberger-Procaccia关联指数检验和BDS检验在区分确定性混沌与随机白噪声上的效果，发现关联指数检验能区分纯混沌与白噪声，但无法区分混有少量白噪声的混沌；BDS检验能正确拒绝混沌数据的独立同分布假设，但可能误拒随机过程。
We consider two ways of distinguishing deterministic time-series from stochastic white noise; the Grassberger—Procaccia correlation exponent test and the Brock, Dechert, Scheinkman (or BDS) test. Using simulated data to test the power of these tests, the correlation exponent test can distinguish white noise from chaos. It cannot distinguish white noise from chaos mixed with a small amount of white noise. With i.i.d. as the null, the BDS correctly rejects the null when the data are deterministic chaos. Although the BDS test may also reject the null even when the data are stochastic, it may be useful in distinguishing between linear and nonlinear stochastic processes.