HOW TO RUN UNIT ROOT TEST USING E-VIEWS SOFTWARE
CHAPTER ONE
INTRODUCTION
1.1 Background of the Study
Empirical identification of asset price bubbles in real time, and even in retrospect, is surely not an easy task, and it has been the source of academic and professional debate for several decades.1 One strand of the empirical literature suggests using time series estimation techniques while exploiting predictions made by finance theory in order to test for the existence of bubbles in the data. The main idea, based on asset pricing theory, suggests that the existence of a bubble component in an observed asset price should be manifested in its dynamics and its stochastic properties. More specifically, theory predicts that if a bubble exists, prices should inherit its explosiveness property. This in turn enables formulating statistical tests aimed at detecting evidence of explosiveness in the data.2 One of the attempts to test for rational bubbles in the context of the stock market is found in Diba and Grossman (1988), where the authors suggest using reduced form stationarity tests with regard to stock prices and observable market fundamentals, and to rule out bubbles if the former is found no more explosive than the latter.
Evans (1991), however, questions the power of such stationarity based tests in the presence of a periodically collapsing bubble (i.e., one that spontaneously occurs and bursts), an apparent feature of actual stock prices seen in the data. Using simulation methods, Evans (1991) shows that standard unit root and cointegration tests fail to reject the null of no bubble in the presence of periodically collapsing bubbles. Despite his findings, Evans (1991) leaves open the question of a better identification strategy. More recently, new bubble detection strategies were developed and presented by Phillips, Wu, and Yu (2011, hereafter PWY) and Phillips, Shi, and Yu (2015, hereafter PSY). These strategies are based on recursive and rolling ADF unit root tests that enable us to detect bubbles in the data and to date-stamp their occurrence.
These types of tests use a right-tail variation of the augmented Dickey-Fuller unit root test wherein the null hypothesis is of