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.
ivInference(
rData,
IVestimator = "RV",
IQestimator = "rQuar",
confidence = 0.95,
alignBy = NULL,
alignPeriod = NULL,
makeReturns = FALSE,
...
)zoo/xts object containing all returns in period t for one asset.
can be chosen among integrated variance estimators: RV, BV, TV, minRV or medRV. RV by default.
can be chosen among integrated quarticity estimators: rQuar, realized tri-power quarticity (TPQ), quad-power quarticity (QPQ), minRQ or medRQ. TPQ by default.
confidence level set by users. 0.95 by default.
a string, align the tick data to "seconds"|"minutes"|"hours"
an integer, align the tick data to this many [seconds|minutes|hours].
boolean, should be TRUE when rData contains prices instead of returns. FALSE by default.
additional arguments.
list
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).
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.
# NOT RUN {
ivInference(sampleTData$PRICE, IVestimator= "minRV", IQestimator = "medRQ",
confidence = 0.95, makeReturns = TRUE)
# }
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