highfrequency (version 0.5)

ivInference:

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, 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.

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)