In this paper, a Nonlinear AutoRegressive network with eXogenous inputs and a support vector machine are proposed for algorithmic trading by predicting the future value of financial time series. These architectures are capable of modeling and predicting vector autoregressive VAR(p) time series. In order to avoid overfitting, the input is pre-processed by independent component analysis to filter out the most noise like component. In this way, the accuracy of the prediction and the trading performance is increased. The proposed algorithms have a small number of free parameters which makes fast learning and trading possible. The method is not only tested on single asset price series, but also on predicting the value of mean reverting portfolios obtained by maximizing the predictability parameter of VAR(1) processes. The tests were first performed on artificially generated data and then on real data selected from exchange traded fund time series including bid-ask spread. In both cases the proposed method could achieve positive returns. Keywords Algorithmic trading • Financial time series • Neural network • Support vector machine • Independent component analysis • Mean reverting portfolio B Attila Ceffer

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In this paper we propose stochastic time series prediction by autoregressive Hidden Markov Models (AR-HMM). The model parameter estimation, hence the prediction, is carried out by Markov chain Monte Carlo (MCMC) sampling instead of finding a single maximum likelihood model. Estimating the whole distribution can provide us with more insight about the underlying stochastic process.As opposed to trading directly on a financial instrument, the predicted future distribution of the underlying asset is then used for option portfolio optimization, where we consider a portfolio of plain vanilla put and call European options with different strike prices. The optimization itself is carried out using linear programming with optional risk constraints.The nature of MCMC sampling of AR-HMMs exhibits algorithmic properties which make a massively parallel implementation feasible and beneficial. The models are implemented using Graphics Processing Units (GPU) to achieve superior performance.The performance of the novel methods has been extensively tested on real financial time series, such as SPY and USO, where they could secure a profit and outperformed the traditional maximum likelihood approaches.

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