# Shiny New Toys

Its been a long time folks, but we have some shiny new toys in the works. Current trends in the industry and working with data scientists has made me a believer in the benefits of using a machine learning approach. I have always been a proponent of “theory-free” approaches on this blog as long as they are designed with robust architecture. In contrast, strict adherence to overly simplistic theories and rules is not optimal for complex systems like the stock market. After experiencing many years of getting whipsawed by traditional indicators, I have recently become convinced a la Philosophical Economics (see this great piece) that you need to have a model(s) that can provide insight into market returns/risk without strictly using price-based indicators. A true macroeconomic model helps to gauge risk that may not be present in current prices and also helps to de-emphasize the reliance price movements that are false alarms. Predicting recessions is not necessarily the most useful for macro models because 1) you can have a bear market without a recession and 2) you can have a recession without a bear market. Furthermore you can have large and damaging corrections that are neither. As a result **predicting drawdowns** is potentially a more interesting and practical exercise.

# S&P 500 Indicator Series

The S&P500 Indicator Series are machine learning forecasting models that use either 1) Macroeconomic 2) Sentiment 3) Technical or 4) Seasonality data with a very wide range of indicators/inputs to make investing decisions.

**S&P 500 Economic Forecasting Model Introduction**

The S&P 500 Economic Forecasting Model employs a Gradient Boosting Model (GBM) to predict the future distribution of S&P500 returns over the next 90 days based on economic data. GBM is a machine learning methodology which can be used for either regression or classification.

The S&P500 Economic Forecasting Model is a classifier model that predicts the likelihood of equity market drawdowns (moderate or large corrections) and the direction of returns (positive, negative or flat) over a 90-day period. The input variables are derivatives of monthly aggregated macroeconomic data, and does not include price-based or technical data. The choice of a classifier model is due to the fact that equity markets are driven by a wide variety of variables that are often nonlinear by nature. Furthermore, it is important to note that macroeconomic variables are just one component that explains the variation in equity market returns and by using a classifier we avoid many of the issues that regression models have with unobserved features.

The model itself is based on an ensemble of GBM style models (specifically using the XGBoost library. A large number of input macroeconomic data series are selected (see Model Importances for the list) and transformed to create derivative time series. Given that monthly economic data is still relatively sparse (60 years of backdata x 12 months/year), we wanted to choose a model technique that doesn’t required huge amounts of data, but is still very flexible. We excluded alternative models such as logistic regression and neural networks for this reason.

In a GBM model that is attempting to match similar periods together, it is important to make the input values ‘comparable’ in some sense, so the raw values are not appropriate in most cases. Otherwise, it is possible for the model to use the values to simply use the values to memorize where it is in time, which does not generalize well. Instead, values are transformed to make them relative (i.e. percentage change Year over Year, or lognormal differences). It is not necessary to make the inputs stationary in a strict sense, but this is useful to maximize the generality of the model.

The models are trained using a k-fold training algorithm, using a Bayesian optimization routine to select the hyperparameters (tree depth, learning rate, etc). Again, this is done to maximize accuracy and generality while avoiding overfitting.

The output of the model is a score, which is then optimized to maximize theMatthews Correlation Coefficient, which can be considered to be a robust accuracy measure for unbalanced classification sets (which the training data in face is).

The model results over time are shown in the chart below. The blue and red bars show the periods where we expect a drawdown of 10%+ (Moderate Correction) or 15%+(Large Correction) respectively *from the end of that period onwards*.

More on this model to follow very soon along with weekly model updates on the predicted output.

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