Periodicity in Intraday log-returns

In search for better measures of volatility, the academics conducted analyses at high and ultra high frequency levels. The seminal works in this field of Andersen and Bollerslev (1997) and Andersen and Bollerslev (1998) paved the way for the following analyses at the intraday levels. We are following the lines of Boudt, Croux and Laurent (2011) and Erdemlioglu, Laurent and Neely (2013) that provided several analyses at the intraday level for the measurement of volatilities and the influence of the continuous, finite jumps and infinite jumps, as in Ait-Sahalia and Jacod (2012), on their evaluation in the presence of periodicity.

In this post we provide an analysis in the form of charts that are meant to be self explanatory. Our main objective is to reveal the periodicity present in the dynamics of the log-returns by looking at several assets and frequencies.

The following presents the dynamics of the average values of prices for each moment of the day, the Autocorrelation Function for simple returns, the Autocorrelation Function for the absolute value of returns and the Autocorrelation Function for the Realized Variance of returns computed for samples of one hour using, for currencies on 1-minute and 5-minute frequencies.


Andersen, T.,G., Bollerslev, T., (1997) Intraday Periodicity and Volatility Persistence in Financial Markets, Journal of Empirical Finance;

Andersen, T.,G., Bollerslev, T., (1998) Deutsche Mark – Dollar Volatility: Intraday Activity Patterns, Macroeconomic Announcements, and Longer Run Dependencies, The Journal of Finance;

Boudt, K., Croux, C., Laurent, S., (2011) Robust Estimation of Intraweek Periodicity in Volatility and Jump Detection, Journal of Empirical Finance;

Erdemlioglu, D., Laurent, S., Neely, C.,J., (2013) Which Continuous-Time Model is Most Appropriate for Exchange Rates?, Research Division, Federal Reserve Bank of Saint Louis, Working Paper Series;

Ait-Sahalia, Y., Jacod, J., (2012) Analyzing the Spectrum of Asset Returns: Jump and Volatility Components in High Frequency Data, Journal of Economic Literature.