Are the Australian and New Zealand stock prices nonlinear with a unit root?

Abstract

Whether or not stock prices are characterized by a unit root has important implications for policy. For instance, by applying unit root tests one can deduce whether stock returns can be predicted from previous changes in prices. A finding of a unit root implies that stock returns cannot be predicted. This paper investigates whether or not stock prices for Australia and New Zealand can be characterized by a unit root process. An unrestricted two-regime threshold autoregressive model is used with an autoregressive unit root. Among the main results, it is found that the stock prices of both countries are nonlinear processes that are characterized by a unit root process, consistent with the efficient market hypothesis.

Acknowledgements

I am grateful to Bruce Hansen for making available his GAUSS codes for the TAR model, which were modified for the present exercise. Helpful comments and suggestions from George Tawadros on an earlier version of this paper are acknowledged. However, any remaining errors are my own.

Notes

¹ Caner and Hansen (2001) show, using Monte Carlo simulations, that when the data generating process has a nonlinear nature and bootstrapped critical values are employed, the R _{1 T} and R _{2 T} tests are more powerful than the conventional ADF test. It should also be noted that several studies (see, inter alia, Caner and Hansen, 2001 and Rodrigues and Gouveia, 2001) have found that the power of the test statistics (R _{1 T} , R _{2 T} , t ₁ and t ₂) increases as nonlinearity becomes more pronounced.