highfrequency (version 0.6.5)

rMPV: Realized multipower variation (MPV), an estimator of integrated power variation.

Description

Function returns the rMPV, defined in Andersen et al. (2012).

Assume there is \(N\) equispaced returns in period \(t\). Let \(r_{t,i}\) be a return (with \(i=1, \ldots,N\)) in period \(t\).

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,
  align.by = NULL,
  align.period = NULL,
  makeReturns = FALSE
)

Arguments

rdata

a zoo/xts object containing all returns in period t for one asset.

m

the window size of return blocks. 2 by default.

p

the power of the variation. 2 by default.

align.by

a string, align the tick data to "seconds"|"minutes"|"hours".

align.period

an integer, align the tick data to this many [seconds|minutes|hours].

makeReturns

boolean, should be TRUE when rdata contains prices instead of returns. FALSE by default.

Value

numeric

References

Andersen, T. G., D. Dobrev, and E. Schaumburg (2012). Jump-robust volatility estimation using nearest neighbor truncation. Journal of Econometrics, 169(1), 75- 93.

Examples

# NOT RUN {
data(sample_tdata)
rMPV(sample_tdata$PRICE, m = 2, p = 3, align.by = "minutes", align.period = 5, makeReturns = TRUE)

# }