Modeling tick-by-tick realized correlations

A tree-structured heterogeneous autoregressive (tree-HAR) process is proposed as a simple and parsimonious model for the estimation and prediction of tick-by-tick realized correlations. The model can account for different time and other relevant predictors’ dependent regime shifts in the conditional mean dynamics of the realized correlation series. Testing the model on S&P 500 Futures and 30-year Treasury Bond Futures realized correlations, empirical evidence that the tree-HAR model reaches a good compromise between simplicity and flexibility is provided. The model yields accurate single- and multi-step out-of-sample forecasts. Such forecasts are also better than those obtained from other standard approaches, in particular when the final goal is multi-period forecasting.