Nonlinear Mean Reversion across National Stock Markets: Evidence from Emerging Asian Markets

Abstract

This paper seeks empirical evidence of nonlinear mean-reversion in relative national stock price indices for Emerging Asian countries. It is well known that conventional linear unit root tests suffer from low power against the stationary nonlinear alternative. Implementing the nonlinear unit root tests proposed by Kapetanios et al. (2003) and Cerrato et al. (2009) for the relative stock prices of Emerging Asian markets, we find strong evidence of nonlinear mean reversion, whereas linear tests fail to reject the unit root null for most cases. We also report some evidence that stock markets in China and Taiwan are highly localized.

Keywords:

• Linear unit root test
• nonlinear unit root test
• nonlinear panel unit root test
• international relative stock prices

JEL CLASSIFICATIONS :

• C22
• G10
• G15

Acknowledgements

We are grateful to Masao Ogaki, Young-Kyu Moh, and the editor for useful comments, and Christopher Vick for excellent research assistance.

Notes

¹If asset prices are mean-reverting, short-selling assets with relatively better performance and buying assets with poor performance in the past may create excess returns. See DeBondt and Thaler (1985).

²For example, Fama and French (1988) and Poterba and Summers (1988) found evidence that favors mean-reversion in US stock prices. Yet, many others questioned the validity of mean-reversion on the robustness issue with regards to the choice of sample period (Kim et al., 1991), the distributional assumptions (Kim et al., 1991; McQueen, 1992), and small sample bias (Richardson and Stock, 1989; Richardson, 1993).

³For example, in the presence of market frictions or transaction costs, arbitrages occur only when the deviations from the fundamental values are big (see, among others; Dumas, 1992; Michael et al., 1997). In other words, when the deviations are relatively small, asset prices may exhibit local nonstationarity around the long-run equilibrium values in the absence of any arbitrage. When dealing with an aggregate price index, a smooth transition model would make more sense, since the transaction costs might be different across the products.

⁴One may test the unit root null for the nominal price deviations from a fundamental variable such as the dividend yield and the price-earning ratio.

⁵Kim (2009) finds similar results for stock price indices of 18 countries with well-developed capital markets.

⁶This is the so-called Davies’ Problem.

⁷Recall, in Section 2, that we construct r _{i, t} as a deviation of individual stock price from its fundamental value. Therefore, f _t can be interpreted as any remaining common shock components that originate from the emerging Asian countries.

⁸For these countries, the observations span from December 1992 ending December 2007.

⁹Note that mean-reversion property is more closely related to the ADF test with an intercept only, since rejecting the unit root null from the ADF test with both intercept and time trend implies that the series is trend stationary. Therefore, the ADF test with both deterministic terms should be understood as a supplementary test when the test with an intercept only does not reject the unit root null.

¹⁰This casts doubt on the results of Balvers et al. (2000) and Chaudhuri and Wu (2004).