Nonlinearities in emerging stock markets: evidence from Europe's two largest emerging markets

Abstract

Recent developments in time series analysis allow proper modelling of nonlinearities in economic and financial variables. A growing body of research was dedicated to investigation of potential nonlinearities in conditional mean of many economic and financial variables, mainly concentrating in developed economies. However, nonlinearities in financial variables in developing economies have not been fully examined yet. In this article we investigate potential nonlinearity and cyclical behaviour of stock returns in Europe's two largest emerging stock markets, mainly in the Greek and Turkish stock markets. Specifically, we use STAR family models, which allow to model nonlinearities in the conditional mean, for modelling monthly returns on stock exchange indices of the Athens Stock Exchange and Istanbul Stock Exchange. Although we find no nonlinearity in conditional variance, we do find strong evidence in favour of nonlinear adjustment of stock returns. It is found that allowing for nonlinearity in conditional mean results in a superior model and provides good out-of-sample forecasts, which contradicts to efficient market hypothesis.

Acknowledgements

We would like to thank professors Erdinc Telatar, Alövset Müslümov, Asli Bayar and Xiaoming Li for their helpful comments and suggestions on the first draft of the article. All remaining errors are our sole responsibility.

Notes

¹In addition, Sarno (2000), Taylor and Sarno (2001), Enders and Chumrusphonlert (2004) and Leon and Najarian (2005), among others, have employed nonlinear models to study nonlinear adjustment of exchange rates in developing countries.

²We also considered lags of the returns, that is y_{t − d} , d=1,…,12, as candidate transition variables. However, linearity was never rejected when the lags of the returns were considered. Therefore, we here report results for long differences only.

³The linear models include dummy variables for outliers evident in the residuals. The linearity tests were also conducted using these dummy variables in order to ensure that rejection of the null of linearity is not due to presence of big outliers. We included the same dummy variables in the estimation of the nonlinear models as well.

⁴We have based our range for threshold value c on observed range of returns by discarding the extreme values at each end.

⁵In estimating the parameters in the STAR models, following Rothman et al . (2001), we have imposed restriction on the value of slope coefficients, namely γ≤500.0, in the transition functions. When the slope coefficient approaches infinity, the STAR model reduces to TAR model. See also van Dijk (1999:8)

⁶The exponential function takes value less than 1 when the annual difference is in the interval from (approximately) −0.03 to 0.03. The logistic function takes value 0 when the bi-monthly difference is less than −0.12 and takes on value 1 when the difference is greater than 0.02.

⁷The forecasts for the ESTAR model were obtained by bootstrapping with 10000 replications. Forecasting with nonlinear models is discussed in Granger and Teräsvirta (1993, Section 8.1) and van Dijk (1999, Section 2.5), among others.