Martingales, the Efficient Market Hypothesis, and Spurious Stylized Facts

TL;DR

This paper argues that apparent stylized facts like fat tails and scaling in financial data are often spurious results caused by nonstationary increments and incorrect assumptions, challenging common beliefs in econophysics.

Contribution

It clarifies how nonstationary increments lead to misleading stylized facts and explains the role of martingale dynamics and nonlinearity in generating these effects.

Findings

Nonstationarity causes spurious fat tails and scaling.

Sliding window techniques produce misleading Hurst exponents.

FX data shows direct evidence of nonstationary increments.

Abstract

The condition for stationary increments, not scaling, detemines long time pair autocorrelations. An incorrect assumption of stationary increments generates spurious stylized facts, fat tails and a Hurst exponent H_s=1/2, when the increments are nonstationary, as they are in FX markets. The nonstationarity arises from systematic uneveness in noise traders' behavior. Spurious results arise mathematically from using a log increment with a 'sliding window'. We explain why a hard to beat market demands martingale dynamics , and martingales with nonlinear variance generate nonstationary increments. The nonstationarity is exhibited directly for Euro/Dollar FX data. We observe that the Hurst exponent H_s generated by the using the sliding window technique on a time series plays the same role as does Mandelbrot's Joseph exponent. Finally, Mandelbrot originally assumed that the 'badly behaved' second moment of cotton returns is due to fat tails, but that nonconvergent behavior is instead direct evidence for nonstationary increments. Summarizing, the evidence for scaling and fat tails as the basis for econophysics and financial economics is provided neither by FX markets nor by cotton price data.