Combining dynamic factor models and artificial neural networks in time series forecasting with applications.

Abstract

This study investigates and examines the advantages and forecasting performance of combining the dynamic factor model (DFM) and artificial neural networks (ANNs) leading to new novel models that have capabilities to produce more accurate forecasts with application to the South African financial sector data. The overall aim of the study is to provide forecasting models that accommodate all relevant variables and the presence of any nonlinearity in the data to produce more adequate forecasts and serve as an alternative to traditional and current forecasting models, particularly in the presence of a changing and interacting environment. The thesis consists of four independent papers corresponding to four chapters. The first chapter brings together two important developments in forecasting literature; the artificial neural networks (ANNs) and factor models. The chapter introduces the Factor Augmented Artificial Neural Network (FAANN) hybrid model in order to produce a more accurate forecasting. The model is applied to forecasting three time series variables, namely, Deposit rate, Gold mining share prices and Long term interest rate. The out-of-sample root mean square error (RMSE) and Diebold-Mariano test results show that the FAANN model yields substantial improvements over the autoregressive AR benchmark model and standard dynamic factor model (DFM). The superiority of the FAANN model is due to the ANNs flexibility to account for potentially complex nonlinear relationships that are not easily captured by linear models. In the second chapter we introduce a new model that exploits the artificial neural networks model as a data smoother to alleviate the effect of major financial crisis and nonlinearity due to high fluctuations such as those associated with the 2008 crisis. The chapter introduces the ANN-DF model, where in the first stage the best fitted ANNs for each single series of the data set which contains 228 monthly series is used to obtain the in-sample forecasts of each series. In the second stage, the factor model is used to extract the factors from the smoothed data set, and then these factors are used as explanatory variables in forecasting. The model is applied to forecast three South Africa variables, namely, Rate on 3-month trade financing, Lending rate and Short term interest rate in the period 1992:01 to 2011:12. The results, based on the root mean square errors of three, six and twelve months ahead out-of-sample forecasts over the period 2007:01 to 2011:12 indicate that, in all of the cases, the ANN-DFM and the DFM statistically outperform the autoregressive (AR) models. In the majority of the cases the ANN-DFM outperforms the DFM. The results indicate the usefulness of smoothing and factor extraction in forecasting performance. The forecast results are confirmed by the test of the equality of forecast accuracy proposed by Diebold-Mariano (1995). The third chapter evaluates the role of the DFM model (liner in nature) and the ANN model (with capacity to handle nonlinearity) as competing forecasting estimation methods. The chapter uses artificial neural networks (ANNs) as nonlinear method based on the fact that the relationships between input and output variables in ANNs do not need to be specified in advance. In this chapter, the same extracted factors are used as input and independent variables for ANNs and the Dynamic Factor Model. This was necessary in order to investigate the forecasting performance of the linear and the nonlinear methods under the same conditions. We refer to the new model as Factor Artificial Neural Network (FANN). The empirical results of the Root Mean Square Error (RMSE) for the out-of-sample forecasts from 2007:01 to 2011:12 indicate that the proposed FANN model is an effective way to improve forecasting accuracy over the Dynamic Factor Model (DFM), the ANN and the AR benchmark model. The results confirm the usefulness of the factors that were extracted from a large set of related variables when we compared the FANN model and the standard univariate ANN model. Finally, combining forecasts is often considered as a successful alternative to using just an individual forecasting method. Different forecasting methods are considered especially when the forecasts are generated form the linear and the nonlinear methods. Thus, chapter four investigates the forecasting performance of combining independent forecasts of the Dynamic Factor Model and the Artificial Neural Networks models using linear and nonlinear combining procedures for the same variables of interest. The analysis was based on three financial variables namely the JSE return index, government bond return index and the Rand/Dollar exchange rate in South Africa. The out-of- sample results of three, six and twelve month horizons from 2006:01 to 2011:12 for the DFM and ANNs provided more adequate forecasts compared to benchmark auto-regressive (AR) models with reduction in the RMSE of around 2 to 12 percent for all variables and over all forecasting horizons. The ANN as a nonlinear combining method outperforms all linear combining methods and is the best individual model for all variables and over all forecasting horizons. The results suggest that the ANN combining method can be used as an alternative to linear combining methods to achieve greater forecasting accuracy. We attribute the superiority of the ANN combining method to its ability to capture any existing nonlinear relationship between the individual forecasts and the actual forecasting values.