Models Part 1: Neural Networks

Introduction

The trading characteristics and ‘behavior’ of a financial instrument in the market is a function of many variables, including: the industry it is in, its current price relative to peers, the type of investors it attracts, its owners and management, its Beta (sensitivity to changes in the market)… and so on. Therefore, different models suit different ETFs. The Reports in this blog are generated after running a pool of models and selecting the model that has the best performance metrics for the selected ETF.  The pool of models are a mix of Artificial Intelligence, Statistical and Econometric models.

This series of articles on Models is intended for investors to have a general understanding of several types of models used in quantitative finance.  

Brief understanding of Neural Networks (NNs)

It is rather difficult to explain how NNs work and for the reader to visualize, but after this brief explanation I will show how a NN model is Run, and all the details required before it is Run, which I hope will give you a better understanding of how NNs are used in financial market forecasting. Probably the best way to understanding NNs is to note that it attempts to mimic the human brain in its structure and the thinking process.

Structure

NNs aim to replicate the neural process in human brains. Our brains function by transmitting electrical impulses through neurons, axons, synapses and dendrites. Electrical impulses jump across synapses when a threshold is crossed. See image below.

Human brain

Artificial NN

Similarly, a NN consists of Neurons and their connections. The input layer are your model variables. Th example in the graphic above consists of 1 output for a forecasting model. In a classification model there will be more than 1 output, 3 input variables and a hidden layer of neurons.  The input neurons pass through the layer of hidden neurons which contain activation functions, which trigger when a threshold is crossed. The connections between all the neurons are weights which are continually adjusted until the cost function is minimized.

Learning

NNs undergo supervised learning in which they are shown their errors and move down a slope until the error margin is at the minimum possible. The error is the difference between their output and what should be the correct answer. The error is backpropagated to the hidden and input layer and the weights adjusted.

Example of a NN being used for modeling an ETF

Data is partitioned into Training, Validation and Testing segments.

Data is rescaled (Standardized)

The NN is trained (it is learning). Here you see the training parameters.

Summary of model performance on testing data. The results are bad. SSE (sum of Squared Errors as well as RMSE (Root Mean Squared Error) are very high.

Median Average Deviation (MAD) as well Coefficient of Correlation (R2 are also terrible)

Residuals (the error, the difference between actual and predicted) during the training session jumps up and down when it should be gradually towards zero.

Reasons for poor results.

1.    NN is not the right model to use for forecasting SPY

2.    With just Open, High and Low as input and Close as output, the NN will tend to overfit.

3.    The output is Close, the absolute price. The NN may do better if asked to forecast % change in Close in the days ahead.

4.    More importantly: A forecasting model cannot be a one-step process.

5.    It must be combined with other statistical and econometric techniques.

6.    The data must be fitted to a suitable Probability Density Function and a Monte Carlo Simulation done to have better results.

Conclusion

It is not so simple. So, beware of supposed financial gurus who tout magic software that can predict the market.  At the most, you can have a sense of the current strength and direction expressed in probabilistic terms.