Classical financial theory and time series forecasting techniques are built upon a normal distribution assumption and suffer from three significant shortcomings:
- Financial assets do not behave according to a normal distribution. Empirical evidence shows that return distributions exhibit jumps, are skewed to the left, have higher peaks and heavier tails than those of the normal distribution
- Return volatilities vary stochastically over time
- Returns and their volatilities are correlated, usually negatively for equities
Lévy Process Models are more flexible distributions and allow to adjust for the above mentioned shortcomings, and result in improved fitting and forecasting accuracy of empirical financial return distributions.
The Pred-X Model uses a wide range of flexible Lévy Process distributions such as Generalized Hyperbolic, Normal Inverse Gaussian or Hyperbolic Processes.
Ensemble methods try to keep or even improve forecasting bias while at the same time increasing robustness and reducing variance. Ensemble methods make predictions according to a combination of base model forecasts and differ in the type of model aggregation scheme utilized.
Ensemble methods are expected to be useful when there is uncertainty in choosing the best model and when it is important to avoid large errors. Both criteria apply to our context of time series forecasting. One necessary condition for an ensemble to be more accurate than any of its individual members is to have diverse and accurate base models, where accurate is defined as having a low bias.
Diverse base models make different errors on new data points and are therefore not perfectly correlated. Hence, the strength of an ensemble depends on the strength of the individual forecasts (in our case based on Lévy process models) and a measure of correlation between their prediction errors on new data.