ivInference: Function returns the value, the standard error and the...

In highfrequency: Tools for Highfrequency Data Analysis

Description

This function supplies information about standard error and confidence band of integrated variance (IV) estimators under Brownian semimartingales model such as: bipower variation, minRV, medRV. Depending on users' choices of estimator (integrated variance (IVestimator), integrated quarticity (IQestimator)) and confidence level, the function returns the result.(Barndorff (2002)) Function returns three outcomes: 1.value of IV estimator 2.standard error of IV estimator and 3.confidence band of IV estimator.

Assume there is N equispaced returns in period t.

Then the ivInference is given by:

\mbox{standard error}= \frac{1}{√{N}} *sd

\mbox{confidence band}= \hat{IV} \pm cv*se

in which,

\mbox{sd}= √{θ \times \hat{IQ}}

cv: critical value.

se: standard error.

θ: depending on IQestimator, θ can take different value (Andersen et al. (2012)).

\hat{IQ} integrated quarticity estimator.

Usage

ivInference (rdata, IVestimator="RV", IQestimator="TPQ", confidence=0.95, 
            align.by= NULL, align.period = NULL, makeReturns = FALSE, ...)

Arguments

rdata	a zoo/xts object containing all returns in period t for one asset.
IVestimator	can be chosen among integrated variance estimators: RV, BV, minRV or medRV. RV by default.
IQestimator	can be chosen among integrated quarticity estimators: rQuar, realized tri-power quarticity (TPQ), quad-power quarticity (QPQ), minRQ or medRQ. TPQ by default.
confidence	confidence level set by users. 0.95 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.

Details

The theoretical framework is the logarithmic price process X_t belongs to the class of Brownian semimartingales, which can be written as:

\mbox{X}_{t}= \int_{0}^{t} a_udu + \int_{0}^{t}σ_{u}dW_{u}

where a is the drift term, σ denotes the spot volatility process, W is a standard Brownian motion (assume that there are no jumps).

Value

list

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.

Barndorff-Nielsen, O. E. (2002). Econometric analysis of realized volatility and its use in estimating stochastic volatility models. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 64(2), 253-280.

Examples

data(sample_tdata)
ivInference(sample_tdata$PRICE, IVestimator= "minRV", IQestimator= "medRQ", 
            confidence=0.95, makeReturns = TRUE)

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