A statistical implementation of feedforward neural networks for univariate time series forecasting

Recently, there has been a growing interest in nonlinear methods for forecasting. As a result, a variety of tests for detecting nonlinearity in univariate series has been developed. However, in order to make predictions, it is not sufficient to uncover nonlinearities, we must describe them through an adequate nonlinear model. Unfortunately, for many applications, theory does not guide the model building process by suggesting the relevant functional form. Thus, forecasters often must rely on a linear approximation or an arduous search for the appropriate nonlinear model.; This difficulty makes it attractive to consider an atheoretical but flexible class of statistical models known as Artificial Neural Networks (ANN). Neural networks can approximate any function up to any desired degree of accuracy. However, in the presence of stochastic noise, this ability as a universal function approximator makes the specification of the neural network model very difficult. Despite the huge amount of theoretical and applied research on neural networks, there is little in terms of a statistical model building paradigm. In addition, even after an ANN is fit, the model offers no information on the relative importance of the input variables or description of the data generating process.; This dissertation presents a new technique for nonlinear time series forecasting which we call STAT-ANN. This method provides the same flexibility as a neural network but has a statistical basis for model selection, interpretation, and validation by following a two-step process: pre-specifying the input basis and performing a nonlinear regression for function approximation. Through simulation, we show that STAT-ANN performs comparably to the true model when the actual data generating process is a known linear or neural network function and that STAT-ANN outperforms other forecasting methods on the Airline and Lynx benchmark time series. We also use these two series to demonstrate the unique descriptive ability of a STAT-ANN model which helps the user better understand the data generating process. A forecasting competition format is used to test the performance of the new method on macroeconomic and financial time series against linear models and the traditional neural network over an increasing forecasting horizon.