# rMPV: Realized multipower variation (MPV), an estimator of... In highfrequency: Tools for Highfrequency Data Analysis

## 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, …,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} ∑_{i=1}^{N-m+1}|r_{t,i}|^{p/m} … |r_{t,i+m-1}|^{p/m}

in which

d_{m,p}= μ_{p/m}^{-m}:

m: the window size of return blocks;

p: the power of the variation;

and m > p/2.

## Usage

 1 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. ... additional arguments.

numeric

## Author(s)

Giang Nguyen, Jonathan Cornelissen and Kris Boudt

## 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

 1 2 data(sample_tdata) rMPV(sample_tdata\$PRICE, m=2, p=3, align.by= "minutes", align.period=5,makeReturns= TRUE) 

highfrequency documentation built on May 31, 2017, 4:34 a.m.