Modeling Financial Time Series with Artificial Neural Networks

Financial time series convey the decisions and actions of a population of human actors over time. Econometric and regressive models have been developed in the past decades for analyzing these time series. More recently, biologically inspired artificial neural network models have been shown to overcome some of the main challenges of traditional techniques by better exploiting the non-linear, non-stationary, and oscillatory nature of noisy, chaotic human interactions. This review paper explores the options, benefits, and weaknesses of the various forms of artificial neural networks as compared with regression techniques in the field of financial time series analysis.CELEST, a National Science Foundation Science of Learning Center (SBE-0354378); SyNAPSE program of the Defense Advanced Research Project Agency (HR001109-03-0001

Localized Lasso for High-Dimensional Regression

We introduce the localized Lasso, which is suited for learning models that are both interpretable and have a high predictive power in problems with high dimensionality $d$ and small sample size $n$. More specifically, we consider a function defined by local sparse models, one at each data point. We introduce sample-wise network regularization to borrow strength across the models, and sample-wise exclusive group sparsity (a.k.a., $\ell_{1,2}$ norm) to introduce diversity into the choice of feature sets in the local models. The local models are interpretable in terms of similarity of their sparsity patterns. The cost function is convex, and thus has a globally optimal solution. Moreover, we propose a simple yet efficient iterative least-squares based optimization procedure for the localized Lasso, which does not need a tuning parameter, and is guaranteed to converge to a globally optimal solution. The solution is empirically shown to outperform alternatives for both simulated and genomic personalized medicine data