Abstract
This paper presents a definition of Multi-Valued Martingale Difference (MVMD) based on Castaing representation of a multi-valued martingale that consists of martingale difference selections. Testing the Multi-Valued Martingale Difference Hypothesis (MVMDH) then examined. Testing the Martingale Difference Hypothesis (MDH) earlier was based on linear measures then later developed two directions in order to account for the existing nonlinearity in economic and financial data. First, the classical approaches have been modified by take into account the possible nonlinear dependence. Second, the use of more sophisticated statistical tools such as those based generalized spectral analysis. According to this article, both these developments in MDH are modified for MVMDH and applies them to exchange rate data and returns of stock market data.
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