View source: R/realizedMeasures.R
rBPCov | R Documentation |
Calculate the Realized BiPower Covariance (rBPCov), defined in Barndorff-Nielsen and Shephard (2004).
Let r_{t,i} be an intraday N x 1 return vector and i=1,...,M the number of intraday returns.
The rBPCov is defined as the process whose value at time t is the N-dimensional square matrix with k,q-th element equal to
\mbox{rBPCov}[k,q]_t = \frac{π}{8} \bigg( ∑_{i=2}^{M} ≤ft| r_{(k)t,i} + r_{(q)t,i} \right| \ ≤ft| r_{(k)t,i-1} + r_{(q)t,i-1} \right| \\ - ≤ft| r_{(k)t,i} - r_{(q)t,i} \right| \ ≤ft| r_{(k)t,i-1} - r_{(q)t,i-1} \right| \bigg),
where r_{(k)t,i} is the k-th component of the return vector r_{i,t}.
rBPCov( rData, cor = FALSE, alignBy = NULL, alignPeriod = NULL, makeReturns = FALSE, makePsd = FALSE, ... )
rData |
an |
cor |
boolean, in case it is |
alignBy |
character, indicating the time scale in which |
alignPeriod |
positive numeric, indicating the number of periods to aggregate over. E.g. to aggregate
based on a 5-minute frequency, set |
makeReturns |
boolean, should be |
makePsd |
boolean, in case it is |
... |
used internally, do not change. |
in case the input is and contains data from one day, an N by 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.
Jonathan Cornelissen, Kris Boudt, and Emil Sjoerup.
Barndorff-Nielsen, O. E., and Shephard, N. (2004). Measuring the impact of jumps in multivariate price processes using bipower covariation. Discussion paper, Nuffield College, Oxford University.
ICov
for a list of implemented estimators of the integrated covariance.
# Realized Bipower Variance/Covariance for a price series aligned # at 5 minutes. # Univariate: rbpv <- rBPCov(rData = sampleTData[, list(DT, PRICE)], alignBy ="minutes", alignPeriod = 5, makeReturns = TRUE) # Multivariate: rbpc <- rBPCov(rData = sampleOneMinuteData, makeReturns = TRUE, makePsd = TRUE) rbpc
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