highfrequency (version 0.8.0)

rMPV: Realized multipower variation

Description

Calculate the Realized Multipower Variation rMPV, defined in Andersen et al. (2012).

Assume there are \(N\) equispaced returns \(r_{t,i}\) in period \(t\), \(i=1, \ldots,N\). Then, the rMPV is given by $$ \mbox{rMPV}_{N}(m,p)= d_{m,p} \frac{N^{p/2}}{N-m+1} \sum_{i=1}^{N-m+1}|r_{t,i}|^{p/m} \ldots |r_{t,i+m-1}|^{p/m} $$

in which

\(d_{m,p} = \mu_{p/m}^{-m}\):

\(m\): the window size of return blocks;

\(p\): the power of the variation;

and \(m\) > \(p/2\).

Usage

rMPV(
  rData,
  m = 2,
  p = 2,
  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.

m

the window size of return blocks. 2 by default.

p

the power of the variation. 2 by default.

alignBy

character, indicating the time scale in which alignPeriod is expressed. Possible values are: "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

numeric

References

Andersen, T. G., Dobrev, D., and Schaumburg, E. (2012). Jump-robust volatility estimation using nearest neighbor truncation. Journal of Econometrics, 169, 75-93.

Examples

# NOT RUN {
mpv <- rMPV(sampleTData[, list(DT, PRICE)], m = 2, p = 3, alignBy = "minutes",
            alignPeriod = 5, makeReturns = TRUE)
mpv
# }