rKurt {highfrequency}

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}.

Usage

rKurt(rData, alignBy = NULL, alignPeriod = NULL, makeReturns = FALSE)

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.

Value

• 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.

Author(s)

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.

Examples

rk <- rKurt(sampleTData[, list(DT, PRICE)], alignBy = "minutes",
            alignPeriod = 5, makeReturns = TRUE)
rk