rCov: Realized covariance

Description

Function returns the Realized Covariation (rCov). Let $r_{t,i}$ be an intraday $N \times M$ return vector and $i=1,...,M$ the number of intraday returns.

Then, the rCov is given by $$ \mbox{rCov}_{t}=\sum_{i=1}^{M}r_{t,i}r'_{t,i}. $$

Usage

rCov(
  rData,
  cor = FALSE,
  alignBy = NULL,
  alignPeriod = NULL,
  makeReturns = FALSE,
  ...
)

Value

in case the input is and contains data from one day, an $N \times N$ matrix is returned. If the data is a univariate xts object with multiple days, an xts is returned. If the data is multivariate and contains multiple days (xts or data.table), the function returns a list containing N by N matrices. Each item in the list has a name which corresponds to the date for the matrix.

Arguments

rData: an xts or data.table object containing returns or prices, possibly for multiple assets over multiple days.
cor: boolean, in case it is TRUE, and the input data is multivariate, the correlation is returned instead of the covariance matrix. FALSE by default.
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.
...: used internally, do not change.

Author

Jonathan Cornelissen, Kris Boudt, and Emil Sjoerup.

Examples

Run this code

# Realized Variance/Covariance for prices aligned at 5 minutes.

# Univariate:
rv = rCov(rData = sampleTData[, list(DT, PRICE)], alignBy = "minutes",
          alignPeriod = 5, makeReturns = TRUE)
rv

# Multivariate:
rc = rCov(rData = sampleOneMinuteData, makeReturns = TRUE)
rc