Lead-Lag Relationship using a Stop-and-Reverse-MinMax Process

Abstract: The intermarket analysis, in particular the lead-lag relationship, plays an important role within financial markets. Therefore a mathematical approach to be able to find interrelations between the price development of two different financial underlyings is developed in this paper. Computing the differences of the relative positions of relevant local extrema of two charts, i.e., the local phase shifts of these underlyings, gives us an empirical distribution on the unit circle. With the aid of directional statistics such angular distributions are studied for many pairs of markets. It is shown that there are several very strongly correlated underlyings in the field of foreign exchange, commodities and indexes. In some cases one of the two underlyings is significantly ahead with respect to the relevant local extrema, i.e., there is a phase shift unequal to zero between these two underlyings.