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

• Main Authors: Christopher Krauss, Klaus Herrmann
• Format: Article
• Language: English
• Published: MDPI AG 2017-02-01
• Series: Journal of Risk and Financial Management
• Subjects: cointegration testing; high-frequency; stylized facts; conditional heteroskedasticity; smooth transition autoregressive models
• Online Access: http://www.mdpi.com/1911-8074/10/1/7

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.