Testing the Martingale Difference Hypothesis
提出一种能同时检测线性和非线性替代假设的鞅差假设检验方法，并采用修正的wild bootstrap程序解决检验统计量渐近分布依赖数据生成过程的问题，通过蒙特卡洛实验验证了有限样本表现。
Abstract In this paper we consider testing that an economic time series follows a martingale difference process. The martingale difference hypothesis has typically been tested using information contained in the second moments of a process, that is, using test statistics based on the sample autocovariances or periodograms. Tests based on these statistics are inconsistent since they cannot detect nonlinear alternatives. In this paper we consider tests that detect linear and nonlinear alternatives. Given that the asymptotic distributions of the considered tests statistics depend on the data generating process, we propose to implement the tests using a modified wild bootstrap procedure. The paper theoretically justifies the proposed tests and examines their finite sample behavior by means of Monte Carlo experiments.