The moving averages demystified

A common method in technical analysis is the construction of moving averages along time series of stock prices. We show that they present a practical interest for physicists, and raise new questions on fundamental ground. Indeed, self-affine signals characterized by a defined roughness exponent H can be investigated through moving averages. The density ρ of crossing points between two moving averages is shown to be a measure of long-range power-law correlations in a signal. Finally, we present a specific transform with which various structures in a signal, e.g. trends, cycles, noise, etc. can be investigated in a systematic way.