Using a Random Walk Model to Justify Technical Analysis of Expectations in Exchange Rate Dynamics

Abstract

This paper examines the derivation of fundamental technical analysis rules based on random walk patterns that emerge from the arcsine law. Specifically, the limiting value of the average time for a random walk to return to the origin is infinite; within a return half-cycle, the first peak occurs near the beginning, whereas the second peak occurs near the end. We analyze support and resistance levels, market trends, (expanded) trading channels, false breakouts, double-bottom and double-top formations, the three-wave and head-and-shoulders patterns, the role of trading volumes and their climaxes, moving averages, overbought and oversold indicators, the comparison of indicators with different volatilities. We correlate these tools with derivatives of various orders. Overall, technical analysis may be interpreted, by structural analogy, as capturing multi-scale price dynamics similar to those formally described by partial differential equations in mathematical physics.