rKurt: Realized kurtosis of highfrequency return series.
Description
Calculate the realized kurtosis as defined in Amaya et al. (2015).
Assume there are \(N\) equispaced returns in period \(t\). Let \(r_{t,i}\) be a return (with \(i=1, \ldots,N\)) in period \(t\).
Then, rKurt is given by
$$
\mbox{rKurt}_{t} = \frac{N \sum_{i=1}^{N}(r_{t,i})^4}{\left( \sum_{i=1}^N r_{t,i}^2 \right)^2}.
$$
In case the input is an xts object with data from one day, a numeric of the same length as the number of assets.
If the input data spans multiple days and is in xts format, an xts will be returned.
If the input data is a data.table object, the function returns a data.table with the same column names as the input data, containing the date and the realized measures.
Arguments
rData
an xts or data.table object containing returns or prices, possibly for multiple assets over multiple days.
alignBy
character, indicating the time scale in which alignPeriod is expressed.
Possible values are: "ticks", "secs", "seconds", "mins", "minutes", "hours"
alignPeriod
positive numeric, indicating the number of periods to aggregate over. For example, to aggregate
based on a 5-minute frequency, set alignPeriod = 5 and alignBy = "minutes".
makeReturns
boolean, should be TRUE when rData contains prices instead of returns. FALSE by default.
Author
Giang Nguyen, Jonathan Cornelissen, Kris Boudt, Onno Kleen, and Emil Sjoerup.
References
Amaya, D., Christoffersen, P., Jacobs, K., and Vasquez, A. (2015). Does realized skewness and kurtosis predict the cross-section of equity returns? Journal of Financial Economics, 118, 135-167.