Nonlinear trend–reversion analysis for earlier centuries

Develop statistically significant nonlinear regression analyses of monthly financial data prior to 1871 to determine how the relationship between future returns and trend strength (including linear and cubic effects) evolved in earlier centuries.

Background

The paper demonstrates a robust nonlinear (cubic) relationship between future returns and trend strength over the period since 1871, consistent with modern daily and intraday findings. The authors aimed to extend this nonlinear analysis further back in time to assess historical evolution of trend persistence and reversion beyond linear effects.

Data quality and availability issues in earlier centuries—such as infrequent price quotes, pegged currencies, hyperinflations, and volatility shifts—impede obtaining statistically significant nonlinear results, leaving the historical dynamics of the nonlinear pattern unresolved.