Testing the martingale hypothesis

Abstract

This chapter examines testing the Martingale difference hypothesis (MDH) and related statistical inference issues. The earlier literature on testing the MDH was based on linear measures of dependence, such as sample autocorrelations; for example, the classic Box-Pierce portmanteau test and the variance ratio test. In order to account for the existing nonlinearity in economic and financial data, two directions have been entertained. First, to modify these classical approaches by taking into account possible nonlinear dependence. Second, to use more sophisticated statistical tools such as those based on empirical process theory or the use of generalized spectral analysis. This chapter discusses these developments and applies them to exchange rate data.