Nonparametric test for a constant beta between \Ito semi-martingales based on high-frequency data

TL;DR

This paper introduces a nonparametric statistical test to determine if the beta coefficient remains constant over time in high-frequency financial data, using asymptotic properties of covariation estimates.

Contribution

It develops a novel nonparametric test for constant beta in high-frequency data, with proven rate optimality over smoothness classes.

Findings

Test is asymptotically valid and rate optimal.

Applicable to high-frequency financial data.

Provides a new tool for dynamic beta analysis.

Abstract

We derive a nonparametric test for constant beta over a fixed time interval from high-frequency observations of a bivariate \Ito semimartingale. Beta is defined as the ratio of the spot continuous covariation between an asset and a risk factor and the spot continuous variation of the latter. The test is based on the asymptotic behavior of the covariation between the risk factor and an estimate of the residual component of the asset, that is orthogonal (in martingale sense) to the risk factor, over blocks with asymptotically shrinking time span. Rate optimality of the test over smoothness classes is derived.