On December 4 , a seminar with the participation of Professor of the Faculty of Economics of the University of Hitotsubashi Eiji Kurozumi will be held at the Gaidar Institute

Professor Kurozumi is a winner of the JSS Outstanding Research Award in 2015 which is awarded by the Statistical Community of Japan. He is known as an econometrics expert whose works are published in journals such as the Journal of Econometrics, Econometric Theory, Econometric Reviews, Econometrics Journal, Journal of Time Series Analysis, Oxford Bulletin of Economics and Statistics, Journal of Statistical Planning and Economics, Letters and others.

We investigate monitoring tests for a bubble. We extend the sup-ADF and generalized sup-ADF tests by Phillips, Wu, and Yu (2011) and Phillips, Shi, and Yu (2015) to the monitoring scheme. We also consider applying the CUSUM detector as proposed by Homm and Breitung (2012). We derive the limiting distributions of the detectors under the null hypothesis, the moderate deviation alternative, and the local alternative. We find that although the moderate deviation alternative gives the difference in the divergence rates of the ADF-type and CUSUM-type detectors, the local asymptotic theory is more useful to understand their difference in details. We also conduct the finite sample simulations and confirm that the local asymptotic theory approximates the finite sample properties of the tests very well.