Testing First Order Autocorrelation: A Simple Parametric Bootstrap Approach to Improve Over the Standard Tests

SYNOPTIC ABSTRACT

To test the existence of first order autocorrelation, the most commonly used method is the Durbin-Watson Test (DWT), and almost all math-stat software/packages have DWT built in them. However, it should be noted that the DWT is a very conservative test and has a very poor power performance for small to moderate sample sizes, apart from being inconclusive sometimes. On this note, we propose a parametric bootstrap (PB) approach to improve upon the DWT. It shows substantial improvements in size and power, even for small samples. It was found that our proposed PB tests perform better than the Lagrange Multiplier Test (LMT), another popular test often used in lieu of the DWT. Hopefully, this work will encourage further interest on this topic, as auto-regression models are widely used in business and economics.

KEY WORDS AND PHRASES:

• Autocorrelation
• bootstrap
• Durbin-Watson test
• power
• size

Additional information

Funding

The first author’s research has been supported partially by a research grant from the Ministry of Science and Technology (MOST 104-2118-M-130-001). For the second author, this research is funded by the Foundation for Science and Technology Development of Ton Duc Thang University (FOSTECT), website: http://fostect.edu.vn. under Grant FOSTECT.2015.BR.20.