Testing the Lag Structure of Assets’ Realized Volatility Dynamics

Abstract

A (conservative) test is applied to investigate the optimal lag structure for modelingrealized volatility dynamics. The testing procedure relies on the recent theoretical results that showthe ability of the adaptive least absolute shrinkage and selection operator (adaptive lasso) to combinee cient parameter estimation, variable selection, and valid inference for time series processes. In anapplication to several constituents of the S&P 500 index it is shown that (i) the optimal significantlag structure is time-varying and subject to drastic regime shifts that seem to happen across assetssimultaneously; (ii) in many cases the relevant information for prediction is included in the first 22lags, corroborating previous results concerning the accuracy and the diffculty of outperforming outof-sample the heterogeneous autoregressive (HAR) model; and (iii) some common features of theoptimal lag structure can be identified across assets belonging to the same market segment or showinga similar beta with respect to the market index.

Keywords

• realized volatility
• adaptive lasso
• HAR model
• test for false positives
• lag structure