Long Run Law and Entropy

TL;DR

This paper develops new long-run laws of unexpected shocks for economic variables using martingale theory, deriving implications for asset pricing without stationarity assumptions, and introduces measures to evaluate asset models.

Contribution

It introduces additive and multiplicative long-run laws based on martingale theory, applicable without stationarity, and proposes dynamic measures to assess asset pricing models.

Findings

New long-run laws of shocks derived without stationarity.

Dynamic measures for asset pricing model diagnostics.

Implications for asset return and pricing kernel analysis.

Abstract

This paper demonstrates the additive and multiplicative version of a long-run law of unexpected shocks for any economic variable. We derive these long-run laws by the martingale theory without relying on the stationary and ergodic conditions. We apply these long-run laws to asset return, risk-adjusted asset return, and the pricing kernel process and derive new asset pricing implications. Moreover, we introduce several dynamic long-term measures on the pricing kernel process, which relies on the sample data of asset return. Finally, we use these long-term measures to diagnose leading asset pricing models.