An Unobserved Components Based Test for Asset Price Bubbles

The general solution of the standard stock pricing equation commonly employed in the finance literature decomposes the price of an asset into the sum of a fundamental price and a bubble component that is explosive in expectation. Despite this, the extant literature on bubble detection focuses almost exclusively on modelling asset prices using a single time-varying autoregressive process, a model which is not consistent with the general solution of the stock pricing equation. We consider a different approach, based on an unobserved components time series model whose components correspond to the fundamental and bubble parts of the general solution. Based on the locally best invariant testing principle, we derive a statistic for testing the null hypothesis that no bubble component is present, against the alternative that a bubble episode occurs in a given subsample of the data. In order to take an ambivalent stance on the possible number and timing of the bubble episodes, our proposed test is based on the maximum of a doubly recursive implementation of this statistic over all possible break dates. Simulation results show that our proposed tests can be significantly more powerful than the industry standard tests developed by Phillips, Shi and Yu (2015).