A survey of models and methods used for forecasting when investing in financial markets

The Makridakis M6 Financial Duathalon competition builds on prior M-competitions that focus on the properties of point and probabilistic forecasts of random variables by also evaluating investment decisions in financial markets. In particular, the M6 competition evaluates both forecasts and investment outcomes associated with the analysis of a large group of financial time series variables. Given the importance of return and risk forecasting when making investment decisions, a natural question in this context concerns what sorts of methods and models are available for said forecasting and were used by participants of the competition. In this survey, we discuss such methods and models, with a specific focus on the construction of financial time series forecasts using approaches designed for both discrete and continuous time setups and using both small and large (high dimensional and/or high frequency) datasets. Examples covered range from simple random walk-type models of returns to parametric GARCH and nonparametric integrated volatility methods for forecasting volatility (risk). We also present the results of a novel empirical illustration that underscores the difficulty in forecasting financial returns, even when using so-called big data.