Forecasting Conditional Variance of S&P100 Returns Using Feedforward and Recurrent Neural Networks

Abstract

It is shown that time series about financial market variables are highly nonlinearly dependent on time. Fluctuations or volatility of returns on assets is one of them. Portfolio managers, option traders and market makers are all interested in volatility forecasting in order to get higher profits and less risky positions. The nonlinear dependence on time is very complex and parametric approaches, and linear models fail. Therefore as nonparametric tools artificial neural networks (ANNs) are candidates to deal with the volatility and/or return forecasting problems. On the other hand, based on the fact that volatility is time varying and that periods of high volatility tend to cluster, the most popular models in modeling volatility are GARCH type models because they can account excess kurtosis and asymmetric effects of financial time series. A standard GARCH(1,1) model usually indicates high persistence in the conditional variance, which may originate from structural changes. Hence it is natural that artificial neural networks (ANN) will be constructed to capture the nonlinear relationship between past return innovations and conditional variance which may be missed by linear regression models. First a usual feedforward, back propagation network is used. The structure of the return data makes FFANN difficult to converge. To overcome this difficulty a neural network with appropriate recurrent connections in the context of nonlinear ARMA models are used. These are the Jordan neural networks (JNN). Then Elman recurrent networks (ENN) and a mixture of the two (EJNN) are also used. The data set consists of returns of the S&P100 index daily closing prices obtained from the S&P100 website. The results indicate that the selected JNN(1,1,1) model has superior performances compared to the standard GARCH(1,1) model. The contribution of this paper can be seen in determining the appropriate NN that is comparable to the standard GARCH(1,1) model and its application in forecasting conditional variance of stock returns. Moreover, from the econometric perspective, NN models are used as a semi-parametric method that combines flexibility of nonparametric methods and the interpretability of parameters of parametric methods.