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

TL;DR

This paper introduces a mathematical method to analyze lead-lag relationships between financial markets by examining local extrema and phase shifts, revealing significant correlations and directional lead-lag patterns across various asset classes.

Contribution

It develops a novel approach using local extrema differences and directional statistics to quantify and analyze lead-lag relationships in financial markets.

Findings

Strong correlations found in foreign exchange, commodities, and indexes.

Identified significant lead-lag phase shifts between market pairs.

Method reveals directional dependencies in market movements.

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.