Big Data Impacts on Stochastic Forecast Models: Evidence from FX Time Series

With the rise of the Big Data paradigm new tasks for prediction models appeared. In addition to the volume problem of such data sets nonlinearity becomes important, as the more detailed data sets contain also more comprehensive information, e.g. about non regular seasonal or cyclical movements as well as jumps in time series. This essay compares two nonlinear methods for predicting a high frequency time series, the USD/Euro exchange rate. The first method investigated is Autoregressive Neural Network Processes (ARNN), a neural network based nonlinear extension of classical autoregressive process models from time series analysis (see Dietz 2011). Its advantage is its simple but scalable time series process model architecture, which is able to include all kinds of nonlinearities based on the universal approximation theorem of Hornik, Stinchcombe and White 1989 and the extensions of Hornik 1993. However, restrictions related to the numeric estimation procedures limit the flexibility of the model. The alternative is a Support Vector Machine Model (SVM, Vapnik 1995). The two methods compared have different approaches of error minimization (Empirical error minimization at the ARNN vs. structural error minimization at the SVM). Our new finding is, that time series data classified as "Big Data" need new methods for prediction. Those new methods should be able to be "customized" to nonlinearity and other non-standard effects, which come along with increasing data volume and can not be standardized to be included in tradional time series models. Estimation and prediction was performed using the statistical programming language R. Besides prediction results we will also discuss the impact of Big Data on data preparation and model validation steps.