Nonlinear modelling of the Finnish Banking and Finance branch index

Abstract

It is well documented that daily returns of several financial assets cannot be modelled by pure linear processes. It seems to be generally accepted that many economic variables follow nonlinear processes. The sources of nonlinearity can be divided in two classes: those where nonlinearities stem from the conditional variance and those where non-linearities enter through the conditional mean. Efforts in modelling the former have resulted in development of the ARCH-family models. There is, however, less evidence on nonlinearity in the mean of financial time series. One family of models that is applied in finance is the STAR. In this paper some nonlinear modelling techniques are applied to a Finnish financial time series, the daily Banking and Finance branch index on the Helsinki Stock Exchange. The techniques include a variance-nonlinear model from the ARCH family, a mean-nonlinear model, namely Smooth Transition Autoregression (STAR)-model and a neural network. Linearity is tested for by standard autocorrelation tests, LM-tests against the specific nonlinear models and the BDS-test. The study provides supplements to a range of earlier research. It demonstrates that the stock series is both linearly and nonlinearly dependent. Adapting an ARCH(3) eliminates the dependencies most satisfactorily. The ARCH-models and STAR-models were estimated using the SHAZAM-package.