New Tools for Understanding Spurious Regressions
提出分析伪回归的新理论工具，利用正交系统表示随机过程，并推广Weierstrass定理以用维纳过程逼近连续函数和随机过程，应用于随机趋势对时间多项式回归和独立随机游走间回归两个经典伪回归案例。
Some new tools for analyzing spurious regressions are presented. The theory utilizes the general representation of a stochastic process in terms of an orthonormal system and provides an extension of the Weierstrass theorem to include the approximation of continuous functions and stochastic processes by Wiener processes. The theory is applied to two classic examples of spurious regressions: regression of stochastic trends on time polynomials, and regressions among independent random walks. It is shown that such regressions reproduce in part and in whole the underlying orthonormal representations.