highfrequency (version 1.0.1)

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, rMinRV, rMedRV. 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: $$\text{standard error}=\frac{1}{\sqrt{N}}\ast sd$$ $$\text{confidence band}=\widehat{IV}\pm cv\ast se$$ in which, $$\text{sd}=\sqrt{\theta \times \widehat{IQ}}$$

$cv:$ critical value.

$se:$ standard error.

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

$\widehat{IQ}$ integrated quarticity estimator.

Usage

IVinference(
  rData,
  IVestimator = "RV",
  IQestimator = "rQuar",
  confidence = 0.95,
  alignBy = NULL,
  alignPeriod = NULL,
  makeReturns = FALSE,
  ...
)

Value

list

Arguments

rData

xts object containing all returns in period t for one asset.

IVestimator

can be chosen among integrated variance estimators: RV, BV, rMinRV or rMedRV. RV by default.

IQestimator

can be chosen among integrated quarticity estimators: rQuar, realized tri-power quarticity (TPQ), quad-power quarticity (QPQ), rMinRQuar or rMedRQuar. TPQ by default.

confidence

confidence level set by users. 0.95 by default.

alignBy

character, indicating the time scale in which alignPeriod is expressed. Possible values are: "ticks", "secs", "seconds", "mins", "minutes", "hours"

alignPeriod

positive numeric, indicating the number of periods to aggregate over. E.g. to aggregate based on a 5 minute frequency, set alignPeriod to 5 and alignBy to "minutes".

makeReturns

boolean, should be TRUE when rData contains prices instead of returns. FALSE by default.

...

additional arguments.

Author

Giang Nguyen, Jonathan Cornelissen and Kris Boudt

Details

The theoretical framework is the logarithmic price process $X_t$ belongs to the class of Brownian semimartingales, which can be written as: $${\text{X}}_t={\int }_0^t{a}_{u}du+{\int }_0^t{\sigma }_{u}d{W}_u$$ where $a$ is the drift term, $\sigma$ denotes the spot vivInferenceolatility process, $W$ is a standard Brownian motion (assume that there are no jumps).

References

Andersen, T. G., Dobrev, D., and Schaumburg, E. (2012). Jump-robust volatility estimation using nearest neighbor truncation. Journal of Econometrics, 169, 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, 253-280.

Examples

if (FALSE) {
library("xts") # This function only accepts xts data currently
ivInf <- IVinference(as.xts(sampleTData[, list(DT, PRICE)]), IVestimator= "rMinRV",
                     IQestimator = "rMedRQ", confidence = 0.95, makeReturns = TRUE)
ivInf
}