On the Power and Size Properties of Cointegration Tests in the Light of High-Frequency Stylized Facts

Abstract

This paper establishes a selection of stylized facts for high-frequency cointegrated processes, based on one-minute-binned transaction data. A methodology is introduced to simulate cointegrated stock pairs, following none, some or all of these stylized facts. AR(1)-GARCH(1,1) and MR(3)-STAR(1)-GARCH(1,1) processes contaminated with reversible and non-reversible jumps are used to model the cointegration relationship. In a Monte Carlo simulation, the power and size properties of ten cointegration tests are assessed. We find that in high-frequency settings typical for stock price data, power is still acceptable, with the exception of strong or very frequent non-reversible jumps. Phillips-Perron and PGFF tests perform best.

Cointegration in high frequency data

“…The question of testing for no cointegration with high frequency data is of practical relevance since some of its stylized facts can lead to significant distortions of the power of the usual tests. In an extensive Monte Carlo experiment, [37] implement ten leading cointegration tests in a variety of set-up tailored with high-frequency features. They use an AR(1) with normal innovations as benchmark, but also look at non-normality effects employing t-distributed innovations, GARCH effects, nonlinearities and price jumps.…”

Cointegration in high frequency data

“…The question of testing for no cointegration with high frequency data is of practical relevance since some of its stylized facts can lead to significant distortions of the power of the usual tests. In an extensive Monte Carlo experiment, [Krauss and Herrmann, 2017] implement ten leading cointegration tests in a variety of set-up tailored with high-frequency features. They use an AR(1) with normal innovations as benchmark, but also look at non-normality effects employing t-distributed innovations, GARCH effects, nonlinearities and price jumps.…”