A Comment on ‘Resolving Spurious Regressions and Serially Correlated Errors’

Long Memory

D. Ventosa-Santaulària

J.E. Vera-Valdés

A.I. Martínez-Olmos




In order to diminish size distortions of the t-test in a time series linear specification, Agiakloglou (Agiakloglou in Empir Econ, 45(3):1361–1366, 2013) proposed to (1) include the first lag of the dependent variable as a regressor or (2) estimate it using the first differences of the variables. He provided finite-sample evidence to support his proposal. In this paper, we extend the Monte Carlo experiment to different data-generating processes and calculate the asymptotic behavior of the modified specifications. We show that including the lag of the dependent variable as a regressor reduces size distortions when the variables are driftless unit roots, but this approach does not hold under the presence of long memory, nonlinearities, or structural breaks.


The version of record can be downloaded here, while the accepted version can be freely downloaded here