## 4 Brief Literature Survey on ANNs Applied to Time Series Modeling
### Forecasting the Economy with Artificial Neural Networks  
It is of great interest to economists to forecast the \"business cycle\". It affects the economic system of any country due to its fluctuations that impact macroeconomic indicators, such as interest rates, housing demand, occupancy rate, demand for manufactured goods, etc. The economic cycle also affects relevant sociopolitical factors, such as the result of a country's presidential elections. Economists use the Gross Domestic Product (GDP) and the Index of Industrial Production (IIP) to track the business cycle [95]. In this contribution, [PERSON] [95] stresses the reasons why macroeconomic modeling and forecasting are challenging tasks:  
* **Macroeconomics is a non-experimental science**. It is a complicated task to observe the behavior of an economy as a whole, and the possibility of carrying out controlled experiments is very remote;
* **Lack of a priori models**. It is not possible to carry out controlled studies on the effects of the influence that qualitative (non-quantifiable) variables have on economic activity, due to the complexities of the economic system;
* **Noise present in data**. This is due to two main causes: the way in which information is collected and the number of unobserved (non-measurable) variables in economics. The presence of noise in short time series makes it difficult to control the variance of the model, requiring highly complex models to predict this type of phenomena;
* **Nonlinearity**. Due to high levels of noise and limited data, neural network models do not capture the nonlinear characteristics of macroeconomic series. In our view, the perceived difficulty in modeling macroeconomic data's nonlinear features is one of the main reasons why many practitioners still use traditional statistical linear techniques to model macroeconomic data (for instance, several official statistics agencies around the world rely on X13 ARIMA-SEATS [142] to generate ARIMA-based forecasts for macroeconomic time series). On the other hand, there is a growing group of researchers who feel that it is worth continuing with investigations of efficient ANN models that take into account nonlinear features of macroeconomic data since ANNs are capable of achieving universal function approximation. For example, [PERSON] [143] applied nonlinear regime change models and artificial neural networks to anticipate the impact of monetary policy shocks on GDP. Neural Network Challenges in Economy  
Moody [95] categorizes several heuristics for ANN model selection and construction, aimed at minimizing expected prediction error. Considered categories are the following:  
_Meta-parameter selection_. Adjusting the regularization parameter can compensate for bias and variance in the forecast, while varying the number of input nodes can compensate for noise and non-stationarity [144]. _Input variable selection and pruning_. The appropriate selection of input variables is essential for the solution of any prediction problem. The set of variables selected must be representative and provide the greatest possible information with the least amount of them [145; 147; 146]. _Model selection and pruning_. Selecting the right size and appropriate network architecture is a key element in controlling the balance between bias and variance. The above involves eliminating unnecessary weights or nodes, choosing the number of hidden units, selecting a connectivity structure, etc. [148; 149; 150; 151]. _Better regularizers._ Regularization of ANNs reduces model variance and minimizes prediction risk, improving model generalization [152; 153]. _Committee forecasts._ Several economic researchers have made forecasts using a forecasting committee. The approach consists of averaging (weighted or unweighted) the predictions of an ensemble of models [144]. _Model interpretation and visualization._ In general, great importance is placed on obtaining accurate forecasts, leaving aside the understanding of the factors that influence these forecasts.