Abstract
The effects of temporal aggregation and choice of sampling frequency are of great interest in modeling the dynamics of asset price volatility. We show how the squared low-frequency returns can be expressed in terms of the temporal aggregation of a high-frequency series. Based on the theory of temporal aggregation, we provide the link between the spectral density function of the squared low-frequency returns and that of the squared high-frequency returns. Furthermore, we analyze the properties of the spectral density function of realized volatility series, constructed from squared returns with different frequencies under temporal aggregation. Our theoretical results allow us to explain some findings reported recently and uncover new features of volatility in financial market indices. The theoretical findings are illustrated via the analysis of both low-frequency daily Standard and Poor’s 500 (S&P 500) returns from 1928 to 2011 and high-frequency 1-min S&P 500 returns from 1986 to 2007.
Highlights
Long-memory processes, especially the possibility of confusing them with structural changes, are of great interest in the field of time series
The results indicate that random level shifts are needed to explain the empirical features documented
For the low frequency data on Standard and Poor’s 500 (S&P 500) returns, one cannot infer whether the noise is stationary long memory
Summary
Long-memory processes, especially the possibility of confusing them with structural changes, are of great interest in the field of time series. McCloskey and Perron (2013) provide simple trimmed versions of the LP estimator, which are consistent and asymptotically normal with the same limiting variance as the standard LP estimator regardless of whether the underlying long/short-memory process is contaminated by level shifts or deterministic trends Using these robust LP estimators, they study the log-squared daily return series of the S&P 500, the Dow Jones Industrial Average (DJIA), the NASDAQ and the AMEX stock market indices, which are examined by Lu and Perron (2010). We analyze the properties of the spectral density function of realized volatility, constructed from the squared returns with different frequencies under temporal aggregation These results will allow us to tackle a second aim and help us explain the following puzzles.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
