RTPVar: Realized tri-power variation of highfrequency return series.

In highfrequency: Tools for Highfrequency Data Analysis

Description

Function returns the rTPVar, 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 rTPVar is given by

\mbox{rTPVar}_{t}=\frac{N}{N-2} ≤ft( 2^{1/3} \frac{Γ ≤ft(5/6\right)}{ Γ ≤ft(1/2\right)} \right)^{-3} ∑_{i=3}^{N} \mbox({|r_{t,i}|}^{2/3} {|r_{t,i-1}|}^{2/3} {|r_{t,i-2}|}^{2/3})

Usage

rTPVar (rdata, align.by=NULL, align.period=NULL, makeReturns=FALSE,...)

Arguments

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

Value

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

data(sample_tdata)
rTPVar(rdata= sample_tdata$PRICE, align.by= "minutes", align.period =5, makeReturns= TRUE)
rTPVar

Example output

Loading required package: xts
Loading required package: zoo

Attaching package: 'zoo'

The following objects are masked from 'package:base':

    as.Date, as.Date.numeric

[1] 2.773664e-09
function (rdata, align.by = NULL, align.period = NULL, makeReturns = FALSE, 
    ...) 
{
    if (hasArg(data)) {
        rdata = data
    }
    multixts = .multixts(rdata)
    if (multixts) {
        result = apply.daily(rdata, rTPVar, align.by, align.period, 
            makeReturns)
        return(result)
    }
    if (!multixts) {
        if ((!is.null(align.by)) && (!is.null(align.period))) {
            rdata = .aggregatets(rdata, on = align.by, k = align.period)
        }
        if (makeReturns) {
            rdata = makeReturns(rdata)
        }
        q = as.numeric(rdata)
        q = abs(rollapply(q, width = 3, FUN = prod, align = "left"))
        N = length(q) + 2
        rTPVar = N/(N - 2) * gamma(1/2)^2/(4 * gamma(7/6)^2) * 
            sum(q^(4/3))
        return(rTPVar)
    }
}
<environment: namespace:highfrequency>

highfrequency documentation built on May 2, 2019, 6:09 p.m.