highfrequency (version 0.4)

ivInference: Function returns the value, the standard error and the confidence band of the integrated variance (IV) estimator.

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: $$\mbox{standard error}= \frac{1}{\sqrt{N}} *sd$$ $$\mbox{confidence band}= \hat{IV} \pm cv*se$$ in which, $$\mbox{sd}= \sqrt{\theta \times \hat{IQ}}$$ $cv:$ critical value. $se:$ standard error. $\theta:$ depending on IQestimator, $\theta$ can take different value (Andersen et al. (2012)). $\hat{IQ}$ integrated quarticity estimator.

Usage

ivInference (rdata, IVestimator="RV", IQestimator="rQuar", 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, TP, QP, minRQ or medRQ. rQuar 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.

Value

• list

Details

The theoretical framework is the logarithmic price process $X_t$ belongs to the class of Brownian semimartingales, which can be written as: $$\mbox{X}_{t}= \int_{0}^{t} a_udu + \int_{0}^{t}\sigma_{u}dW_{u}$$ where $a$ is the drift term, $\sigma$ denotes the spot volatility process, $W$ is a standard Brownian motion (assume that there are no jumps).

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)