Estimation of continuous time models for the Norwegian thinly traded equity market

The Norwegian market shows relative low trading frquency compared to similar international markets. Solibakke, 1998 finds small differences in the return characteristics (mean and volatility) between thinly and frequently traded stocks on the Norwegian stock exchange using hypothesis tests from a general geometric Brownian motion; that is a classical stochastic differential equation specification. This study set out to determine the quality and the needed complexity of a general SDE model specification for the Norwegian market. Efficient Method of Moments (EMM) is used to estimate and test continuous time diffusion models for a value weighted Norwegian equity index return series. EMM matces to the score of a model determined by data analysis called the score generator (SNP). Novel score models show similarities that reveals characteristics of data that stochastic differential equations (SDE) can approximate (Gallant, Hsieh and Tauchen, 1997). Using adjusted return series from the emerging Norwegian equity market, reveals that both simple and more elaborate score models, following the Schwarz model selection criterion (Schwarz, 1978), show similarities that reveal characteristics of data that a stochastic differential equation (SDE) can approximate. To show these similarities for our index return series I employ four score generators. The simplest score models is the Gaussian ARCH specification. I employ two intermediate specifications. The first is a simple Semiparametric ARCH Score and the second is an elaborate Semiparametric ARCH specification. The ARCH specification is often found in international finance literature. Finally, the fourth model specification which should model the full complexity of the Norwegian market dynamics, is the nonlinear non-parametric specification. The elaborate semi-parametric ARCH Score is preferred using the Schwarz model selection criterion (BIC) (Schwarz, 1978) in our non-parametric time series analysis. However, standard nonlinear tests reveal non-linearity in this elaborate semi-parametric ARCH time series. The nonlinear non-parametric Score model removes all non-linearity using standard tests. For all four score specifications a standard stochastic differential equation with constant volatility is strongly rejected. However, a simple one-factor stochastic volatility specification cannot be rejected in any model, with a possible exception for the nonlinear non-parametric model. Hence, a simple extension for asymmetry suggested by the conditional variance profile from the nonlinear non-parametric score generator, is employed. The extension produces a remarkably good fit for the full complexity of the Norwegian thinly traded equity market. That is, a two equation stochastic volatility SDE, with induced correlation between the mean and volatility, describes the Norwegian index series. The result is both convenient and satisfactory for the Norwegian market. In contrast, similar analysis (for other and longer time periods) in US suggest that the required extensions for a fit to a nonlinear non-parametric score are so elaborate that a non-parametric specification are probably more convenient and probably most satisfactory.