Statistical Learning for Financial Time Series

Given a time series of returns for a portfolio of financial instruments, develop a model that accurately predicts returns which maximize profits. The objective function will take an input of financial indicators from the previous time interval and the returns from the current time interval. These indicators can explain relationships between financial instruments in the portfolio of interest, thus are important for explaining their returns and associated risk. A common challenge with these types of problems is how easy it can be to over-fit your model.

Exploring optimal trading rules in a high-frequency portfolio

Given a set of financial instruments with inherent characteristics at different time intervals, we are interested in finding an optimal trading rule in a high-frequency trading context. A trading rule is defined as a combination of indicators as well as an entry threshold (and potentially other trading parameters). The objective function we are trying to maximize is the profits of the strategy based on the trading rule. One impact of the non-linearity of such problems is that the gradient of the objective function is hard to estimate using a black-box approach.