Lassoing the HAR model: A Model Selection Perspective on Realized Volatility Dynamics

Realized volatility computed from high-frequency data is an important measure for many applications in finance and its dynamics have been widely investigated. Recent notable advances that perform well include the heterogeneous autoregressive (HAR) model which can approximate long memory, is very parsimonious, is easy to estimate, and features good out-of-sample performance.
We prove that the least absolute shrinkage and selection operator (lasso) recovers the lags structure of the HAR model asymptotically if it is the true model, and we present Monte Carlo evidence in finite samples. The HAR model's lags structure is not fully in agreement with the one found using the lasso on real data. Moreover, we provide empirical evidence that there are two clear breaks in structure for most of the assets we consider. These results bring into question the appropriateness of the HAR model for realized volatility. Finally, in an out-of-sample analysis we show equal performance of the HAR model and the lasso approach.