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*.

1 |

`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

Giang Nguyen, Jonathan Cornelissen and Kris Boudt

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

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

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