This study tests for the sandwich-form asymptotic covariance matrices entailed by conditionally heteroskedastic and/or autocorrelated regression errors or conditionally uncorrelated homoskedastic errors. In doing so, we enable the empirical researcher to estimate the asymptotic covariance matrix of the quasi-maximum likelihood estimator by supposing a possibly misspecified model for error distribution. Accordingly, we provide test methodologies by extending the approaches in Cho and White (in: Chang Y, Fomby T, Park JY (eds) Advances in econometrics: essays in honor of Peter CB Phillips. Emerald Group Publishing Limited, West Yorkshire, 2014) and Cho and Phillips (J Econ 202:45–56, 2018a) to detect the influence of heteroskedastic and/or autocorrelated regression errors on the asymptotic covariance matrix. In particular, we establish a sequential testing procedure to achieve our goal. We affirm the theory on our test statistics through simulation and apply the test statistics to energy price growth rate data for illustrative purposes; here, we also apply our test methodology to test the fully correct model hypothesis.
Bibliographical noteFunding Information:
The Editor-in-Chief, Jesús López-Fidalgo, the associate editor, and two anonymous referees provided very helpful comments for which we are most grateful. The authors benefitted from discussions with the seminar participants at BIT. The responsibility for any errors and shortcomings in this work remains ours. Cho is grateful for the research Grant by the Ministry of Education in the Republic of Korea and the National Research Foundation of Korea (NRF-2018S1A5A2A01035256). Huo is grateful for the research Grant support by National Natural Science Foundation of China (No.71803009) and MOE Project of Humanities and Sciences (No. 17YJC790057).
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Statistics, Probability and Uncertainty