Robust analysis of the martingale hypothesis

The martingale hypothesis is commonly tested in financial and economic time series. The existing tests of the martingale hypothesis aim at detecting some aspects of nonstationarity, which is considered an inherent feature of a martingale process. However, there exists a variety of martingale processes, some of which are nonstationary like the well-known random walks, and others are stationary with fat-tailed marginal distributions. The stationary martingales display local trends and bubbles, and can feature volatility induced “mean-reversion” like many observed financial and economic time series. This paper introduces nonparametric tests of the martingale hypothesis, which are robust to the type of martingale process that generated the data and are valid for nonstationary as well as stationary martingales. A new regenerative block bootstrap is introduced as an adjustment method for size distortion of the test in finite sample.