Testing for Nonlinear Autoregression
提出两种检验经济时间序列条件均值是否线性的方法（Cramér–von Mises和Kolmogorov–Smirnov检验），使用自助法估计非标准渐近分布，并通过蒙特卡洛实验和五组美国月度数据验证，发现个人收入和失业率存在非线性，而汇率、利率和货币供给则没有。
This article considers consistent testing the null hypothesis that the conditional mean of an economic time series is linear in past values. Two specific tests are discussed, the Cramér–von Mises and the Kolmogorov–Smirnov tests. The particular feature of the proposed tests is that the bootstrap is used to estimate the nonstandard asymptotic distributions of the test statistics considered. The tests are justified theoretically by asymptotics, and their finite-sample behaviors are studied by means of Monte Carlo experiments. The tests are applied to five U.S. monthly series, and evidence of nonlinearity is found for the first difference of the logarithm of the personal income and for the first difference of the unemployment rate. No evidence of nonlinearity is found for the first difference of the logarithm of the U.S. dollar/Japanese Yen exchange rate, for the first difference of the 3-month T-bill interest rate and for the first difference of the logarithm of the M2 money stock. Contrary to typically used tests, the proposed testing procedures are robust to the presence of conditional heteroscedasticity. This may explain the results for the exchange rate and the interest rate.