An empirical study of neural networks for trend detection in time series

We have derived theoretical maximum likelihood estimators of trends for standard dynamics and implemented them. We have reframed the problem of trend detection into a classification problem amenable to machine learning methods. We have shown that RNN are in a way a generalization of simple moving average techniques and motivated this by theory. In a simple case, we have shown that this generalization transforms the trend estimation problem into simply locating the state vector into convex polytopes cells. Finally, we have showed empirically that GRU or LSTM cells are on average the best building block to use compared to a broad range of estimators in order to detect trends in time series. Putting the emphasis on learning stylized data and then transferring to real data rather than building complex structures fitted to data is also an important takeaway of this paper. Ongoing preliminary research seems to validate our approach for financial applications. This might pave the way to building efficient market estimators protected against over-fitting.