Martingales in Daily Foreign Exchange Rates: Evidence from Six Currencies against the Lebanese Pound

Abstract

The purpose of this paper is to test whether the Lebanese foreign exchange rate market is weak form efficient by studying the stochastic behavior of six foreign currencies against the Lebanese pound on a daily basis. Efficiency requires that the data meet more than one condition. The first condition is the presence of a unit root process. The second one is that increments are random and uncorrelated. The third is the long term persistence of shocks. The fourth is the absence of breaks in the samples. The last one is the insignificance of pair-wise Granger causality tests. These five conditions describe a statistical behavior known as a martingale. All five conditions are found to apply to the six data series. Non-normality, conditional heteroscedasticity, other non-linear dependencies, and contemporaneous cross-correlations of the log returns of the exchange rates are features that are present in the data but that do not invalidate the general designation of a martingale. Finally, the descriptive statistics of the six series under consideration are quite similar to those of other major currencies, even when compared for different time periods, implying that daily foreign exchange rates share quasi the same characteristics globally.