Econometric tests for nonlinear exuberance in economics and finance

Abstract

Exuberant behaviors (bubbles) in economic and financial activities have long been a concern in the literature. In this thesis, we focus on developing econometric tests to detect the existence and to identify the origination and termination dates of this behavior. These econometric tests generalize two existing tests, namely the Markov-switching unit root test of Hall, Psaradakis and Sola (1999, HPS hereafter) and the sup Augmented Dickey-Fuller (ADF) test of Phillips, Wu and Yu (2011, PWY hereafter). Both tests aim to capture the explosive behavior of exuberance under the influence of its periodically collapsing characteristic (Blanchard, 1979). The Markov-switching unit root test combines a right-tailed unit root test (Diba and Grossman, 1988) with the Markov-switching model of Hamilton (1989). The sup ADF test implements the right-tailed ADF test repeatedly on a forward expanding sample sequence.

In the second chapter, we demonstrate that the constant variance assumption in the Markov-switching ADF test of HPS may result in the misjudgment of bubbles. Upon relaxing this assumption to allow for regime-varying error variances in the Markov-switching ADF test (referred to as the MSADF-RV test), we revisit the integration properties of the money base, consumer price and exchange rate in Argentina from January 1983 to November 1989. Using the MSADF-RV test, we observe the occurrence of volatility switches in the exchange rate and the consumer prices instead of observing bubbles in these two series as identified in HPS.

The third chapter discusses the right-tailed unit root test. Right-tailed unit root tests have proved promising for detecting exuberance in economic and financial activities. Like left-tailed tests, the limit theory and test performance are sensitive to the null hypothesis and the model specification used in parameter estimation. This chapter aims to provide some empirical guidelines for the practical implementation of right-tailed unit root tests, focussing on the sup ADF test of PWY, which implements a right-tailed ADF test repeatedly on a sequence of forward sample recursions. We analyze and compare the limit theory of the sup ADF test under different hypotheses and model specifications. The size and power properties of the test under various scenarios are examined in simulations and some recommendations for empirical practice are given. An empirical application to NASDAQ data reveals the practical importance of model specification on test outcomes.

In the fourth chapter, we demonstrate that the complexity of the nonlinear structure in multiple bubble phenomena diminishes the discriminatory power of existing tests. In particular, when there are multiple collapsing bubble episodes within the same sample period, the sup ADF test of PWY may fail to reveal the existence of bubbles. To assist performance in such contexts, the present chapter proposes a generalized version of the sup ADF test to addresses this difficulty. The asymptotic distribution of the generalized sup ADF test is provided and this test is shown to significantly improve power in simulations. In addition, we put forward a date-stamping strategy for the origination and termination of multiple bubbles based on the generalized sup ADF test. Given the data generating process of Phillips and Yu (2009), in which there is a single bubble in the sample period, we show the consistency of the date-stamping strategy. It is further demonstrated that the new strategy leads to distinct power gains over the date-stamping strategy of PWY when there are two bubbles in the sample period. An empirical application is conducted with both tests along with their respective date-stamping strategies to Hong Kong stock market data from October 1980 to September 2009. The generalized sup ADF test finds evidence of bubble existence in the Hang Seng Index over the period from November 2006 to June 2008, whereas the sup ADF test finds no evidence of the presence of bubbles. Show more