# Statistical Models

## Definition

**Statistical Models** denotes a very broad category of models that are primarily based on empirical (historical) data. The class encompasses econometric models, regression models, Machine Learning, predictive models , typical VaR models etc.

The behaviour of the data is systematized in a mathematical model, usually by making some essential assumptions about what is the underlying distribution (parametric models) but with minimal assumptions if sufficient volumes of data are available (non-parametric models)

Examples on non-statistical models are the variety of Structural Models and the No-arbitrage pricing Models where various logical constructs (e.g. causal relations, constraints) are included in the model as opposed to be inferred from data.

## Issues and Challenges

- Availability and quality of historical data
- Correlation versus Causation
- Forward looking applicability