Department Seminar Series: Mohitosh Kejriwal, Associate Professor, Department of Economics, Purdue University

This paper studies the asymptotic properties of least squares estimators for the origination and termination of explosive behavior in a time series. Such estimators are useful for dating the onset and collapse of asset pricing bubbles, an issue of prime importance for policymakers. The dating estimators are based on an autoregressive model in which the origination is modeled as a switch from unit root to explosive behavior while a collapse is indicated by a switch back to unit root behavior. The case where explosivity continues till the end of the sample is also considered. We Örst show that when the break magnitude is Öxed, consistency of the break date estimators only requires the duration of the explosive regime to increase with the sample size. In particular, it is not necessary to assume that the duration is a positive fraction of the sample size, as is typically assumed in the change-point literature. Further, consistency is derived with respect to the break dates and not just the break fractions. To derive the rate of convergence and the ensuing limit distribution, we adopt a mildly explosive representation whereby the break magnitude decreases to zero as the sample size increases. Under certain restrictions on the rate of decrease, we obtain a sharp rate of convergence as well as a tractable limit distribution for the break date estimators based on which conÖdence intervals can be constructed.

[joint work with Pierre Perron, Boston University]