Temporal Aggregation and Long Memory for Asset Price Volatility

摘要

The effects of temporal aggregation and choice of sampling frequency are of great interestin modeling the dynamics of asset price volatility. We show how the squared low-frequency returnscan be expressed in terms of the temporal aggregation of a high-frequency series. Based on the theoryof temporal aggregation, we provide the link between the spectral density function of the squaredlow-frequency returns and that of the squared high-frequency returns. Furthermore, we analyzethe properties of the spectral density function of realized volatility series, constructed from squaredreturns with different frequencies under temporal aggregation. Our theoretical results allow us toexplain some findings reported recently and uncover new features of volatility in financial marketindices. The theoretical findings are illustrated via the analysis of both low-frequency daily Standardand Poor’s 500 (SP 500) returns from 1928 to 2011 and high-frequency 1-min SP 500 returns from1986 to 2007.