Improved sparse mean reverting portfolio selection using simulated annealing and extreme learning machine

We study the problem of selecting a sparse, mean reverting portfolio from a universe of assets using simulated annealing (SA). Assuming that assets follow a first order vector autoregressive process (VAR(1)), we make a number of improvements in existing methods. First, we extend the underlying asset dynamics to include a time-independent additive term, thereby enriching the model's applicability. Second, we introduce Extreme Learning Machine (ELM) to decide whether to apply SA or settle for the much faster greedy solution. Finally, we improve the SA method by better calibration of the initial temperature and by determining the exact value of the weights within a selected dimension using the Rayleigh quotient. On real data, these changes result in more than 90% improvement in run time on average and 4.78% improvement in optimized mean reversion in our simulations. We also test the trading performance of our method on both simulated and real data and managed to achieve positive mean trading results in both cases.