Consider the following idea for the cross-sectional statistical arbitrage: if we have information that forecasts stocks returns then the change in this information also forecasts returns.
For example, we can consider usage of neural networks to calculate difference in information:
1) take some score as the basis (it could be price to earnings and etc)
2) for day t create dataset containing N predictors with K + 1 rows:
score_stock_1(t) … score_stock_N_(t)
…............................................................................
score_stock_1(t - K) … score_stock_N_(t - K)
3) set target for example to [1, 0 … 0], K zeros
4) use neural network to regress this target on the specified predictors, process of learning neural network parameters results in learning the difference in the forecasting data
5) calculate impulse response of the non-linear estimator by feeding N x N identity matrix to neural network, after demeaning and normalization treat this impulse response as weights of long-short portfolio
6) reiterate 2-5 to get weights for each day
This approach is essentially based on the idea of pure factor portfolios. So the results would be rather similar to:
statistical arbitrage, volume factor
You can find pure factor porfolio idea in the corresponding articles by Jose Menchero.
