Trading sparse, mean reverting portfolios using VAR(1) and LSTM prediction

We investigated the predictability of mean reverting portfolios and the VAR(1) model in several aspects. First, we checked the dependency of the accuracy of VAR(1) model on different data types including the original data itself, the return of prices, the natural logarithm of stock and on the log return. Then we compared the accuracy of predictions of mean reverting portfolios coming from VAR(1) with different generative models such as VAR(1) and LSTM for both online and o ine data. It was eventually shown that the LSTM predicts much better than the VAR(1) model. The conclusion is that the VAR(1) assumption works well in selecting the mean reverting portfolio, however, LSTM is a better choice for prediction. With the combined model a strategy with positive trading mean profit was successfully developed. We found that online LSTM outperforms all VAR(1) predictions and results in a positive expected profit when used in a simple trading algorithm.