A Tutorial on Applying Artificial Neural Networks and Geometric Brownian Motion to Predict a Stochastic Time Series

Several challenges in the engineering or financial world can be resolved with a proper handle on data. Amongst other applications in engineering, system identification and parameter estimation are widely used in developing control strategies for automation. In this domain, there would be requirements to design an adaptive control system. In order to design an adaptive control system, an adaptive model needs to be estimated or identified. This is generally done by studying the data and creating a transfer function. In the process, regression, artificial neural networks (ANN), random walk theory and Markov chain estimates are used to understand a time series and create a model. While some of these processes are stationary, some are non-stationary. These methods are chosen based on the nature and availability of historical data. One of the issues that always remain is which method is appropriate for a certain application. The objective of this tutorial is to illustrate how artificial neural network and Geometric Brownian motion can be used in this regard. An attempt is made to predict the future price of a stock of a corporation. Stock prices are an example for a stochastic time series. Initially, an artificial neural network is used to predict the stock price. The network is designed as a Multi layer Back propagation type network. Profit over earnings and S&P are used as inputs. Thereafter, Geometric Brownian motion is explained and used on the same dataset to come up with its predictions. The results from both neural network and geometric Brownian motion are compared.