# Stock Market Crisis Forecasting Using Neural Networks with Input Factor Selection
###### Abstract  
Artificial neural networks have gained increasing importance in many fields, including quantitative finance, due to their ability to identify, learn and regenerate non-linear relationships between targets of investigation. We explore the potential of artificial neural networks in forecasting financial crises with micro-, macroeconomic and financial factors. In this application of neural networks, a huge amount of available input factors, but limited historical data, often leads to over-parameterized and unstable models. Therefore, we develop an input variable reduction method for model selection. With an iterative walk-forward forecasting and testing procedure, we create out-of-sample predictions for crisis periods of the $&P 500 and demonstrate that the model selected with our method outperforms a model with a set of input factors taken from the literature.  
early warning system; financial crisis; neural networks +
Footnote †: journal: Medical  
identification of market crises based on Markov-switching models, as suggested by [14]. Extensions incorporate input variables to receive an appropriate forecast (see, e.g., [15]). Using the Akaike information criterion (AIC), [15] selects a logistic regression model from a larger set of input factors to forecast stock market regimes. A comprehensive overview of various methods and publications for early warning systems can be found in [5]. These approaches include machine learning, in particular neural networks. For example, [16] presents a machine learning forecasting model for financial crises based on three input factors for the forecast. However, the choice of the input factors is not based on an objective method here.  
As pointed out above and in the mentioned literature, we observe that neural networks are well-suited to detect and depict non-linear relations between input data and time series which shall be predicted. With this ability, the model is less subjective than a forecasting model with the structure being defined by a human expert. Unfortunately, as the examples show, achieving this objectivity is far more difficult when it comes to the selection of the input variables itself. An objective variable selection process for a regression model is presented in [15]. One common technique to reduce input factors in neural network models is based on the output sensitivity (see e.g., [17; 18]). The underlying idea is to remove input factors which do not contribute much to the output. However, this creates, in particular for financial data, the problem that variables which do not change much from one month to another, but which might provide valuable information over an economic cycle (such as key interest rates from central banks), or factors with a lower frequency of publication, could be disregarded.  
Faced with the described challenges of the application of neural networks for financial time series analysis, we aim to demonstrate an efficient method of input factor reduction and a rigorous testing mechanism. By pruning variables that have less explanatory significance compared to others, we enable our neural network to avoid unfavorable local minima, mitigate over-parameterization, get closer to the globally optimal points, and return a more stable network (see, e.g., [17; 19]). We begin by introducing the method for the determination of the financial crises for the 5&P 500 index in Section 2. Afterwards, we present the whole set of micro-, macroeconomic and financial input factors in Section 3, to which we apply our input factor reduction method. The architecture of the neural networks we use and our input factor reduction method, are introduced in Section 4. In Section 5, we apply this method to select a subset of the input factors (from Section 3) to forecast crisis states (as introduced in Section 2). The chosen models are tested using a walk-forward testing of out-of-sample predictions in Section 6. We conclude in Section 7.