highfrequency (version 0.5.3)

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

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 \(i=1, \ldots,N\)) in period \(t\).

Then, the rTPVar is given by $$ \mbox{rTPVar}_{t}=\frac{N}{N-2} \left( 2^{1/3} \frac{\Gamma \left(5/6\right)}{ \Gamma \left(1/2\right)} \right)^{-3} \sum_{i=3}^{N} \mbox({|r_{t,i}|}^{2/3} {|r_{t,i-1}|}^{2/3} {|r_{t,i-2}|}^{2/3}) $$

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

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