Long-horizon return predictability from realized volatility in pure-jump point processes

Thomas M. Menino Convention & Exhibition Center 

A novel methodology is developed and justified to consistently test for long-horizon
return predictability based on realized variance. To accomplish this, a parametric
transaction-level model is proposed 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 empirical finance. Under the 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. An
asymptotic framework using power-law aggregation is also proposed in the predictive
regression. Within this framework, a hypothesis test is proposed for long-horizon return
predictability which is asymptotically correctly sized and consistent.

Return predictability

Long memory

Predictive regression

Point process

High frequency 

Business and Economic Statistics Section