Publication Type

Journal Article

Version

publishedVersion

Publication Date

1-2026

Abstract

Asset prices are commonly represented as a drift-diffusion process, wherein the drift component denotes the anticipated return of the asset within some time frame, while the diffusion component accommodates random shocks. The drift component has substantial practical significance but accurate estimation is typically challenging and has met with limited success in the existing literature except over large time spans. This paper explores a comprehensive range of drift-diffusion models that include constant, linear, trending, and bursting drift. Conditions are identified under which realized squared drift  is a reliable tool for gauging integrated squared drift when the time span Tn is large enough. The recently introduced drift-robust quarticity estimator  is found to retain consistency under twin asymptotics with Tn → ∞ and infill Δn → 0, subject to some constraints on the divergence rate of Tn across different drift specifications. An inferential method of detecting nonzero drift using  and  is proposed and the drift tests are shown to be consistent under different data generating processes with various conditions on Tn. Simulation studies reveal excellent performance of the realized squared drift measure and the drift test in finite samples. The drift test is demonstrated empirically in real-time surveillance of market abnormalities in the Nasdaq Composite Index over two notable sample periods: the dotcom bubble (1996–2003) and the artificial intelligence boom (2016–2024), using intraday data.

Keywords

Double asymptotic, Drift diffusion process, Intraday high frequency data, Realized drift, Realized quarticity

Discipline

Econometrics

Research Areas

Econometrics

Publication

Journal of Econometrics

Volume

253

First Page

1

Last Page

29

ISSN

0304-4076

Identifier

10.1016/j.jeconom.2025.106177

Publisher

Elsevier

Additional URL

https://doi.org/10.1016/j.jeconom.2025.106177

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