Long-Horizon Return Predictability from Realized Volatility in Pure-Jump Point Processes

TL;DR

This paper introduces a new methodology for testing long-horizon return predictability using realized variance, based on a pure jump point process model that captures key empirical features of financial data.

Contribution

It develops a parametric transaction-level model with a consistent testing framework for long-horizon return predictability based on realized variance.

Findings

The model aligns with stylized facts in empirical finance.

The proposed test is asymptotically correctly sized and consistent.

Long-memory parameter propagates from transaction level to returns.

Abstract

We develop and justify methodology to consistently test for long-horizon return predictability based on realized variance. To accomplish this, we propose a parametric transaction-level model for the continuous-time log price process based on a pure jump point process. The model determines the returns and realized variance at any level of aggregation with properties shown to be consistent with the stylized facts in the empirical finance literature. Under our model, the long-memory parameter propagates unchanged from the transaction-level drift to the calendar-time returns and the realized variance, leading endogenously to a balanced predictive regression equation. We propose an asymptotic framework using power-law aggregation in the predictive regression. Within this framework, we propose a hypothesis test for long horizon return predictability which is asymptotically correctly sized and consistent.