rKernelCov: Realized kernel estimator

In jonathancornelissen/highfrequency: Tools for Highfrequency Data Analysis

Realized kernel estimator

Description

Realized covariance calculation using a kernel estimator. The different types of kernels available can be found using listAvailableKernels.

Usage

rKernelCov(
  rData,
  cor = FALSE,
  alignBy = NULL,
  alignPeriod = NULL,
  makeReturns = FALSE,
  kernelType = "rectangular",
  kernelParam = 1,
  kernelDOFadj = TRUE,
  ...
)

Arguments

rData	an xts or data.table object containing returns or prices, possibly for multiple assets over multiple days
cor	boolean, in case it is TRUE, and the input data is multivariate, the correlation is returned instead of the covariance matrix. FALSE 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. For example, 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.
kernelType	Kernel name.
kernelParam	Kernel parameter.
kernelDOFadj	Kernel degree of freedom adjustment.
...	used internally, do not change.

Details

Let r_{t,i} be N returns in period t, i = 1, …, N. The returns or prices do not have to be equidistant. The kernel estimator for H = \code{kernelParam} is given by

γ_0 + 2 ∑_{h = 1}^H k ≤ft(\frac{h-1}{H}\right) γ_h,

where k(x) is the chosen kernel function and

γ_h = ∑_{i = h}^N r_{t,i} \times r_{t,i-h}

is the empirical autocovariance function. The multivariate version employs the cross-covariances instead.

Value

in case the input is and contains data from one day, an N by N matrix is returned. If the data is a univariate xts object with multiple days, an xts is returned. If the data is multivariate and contains multiple days (xts or data.table), the function returns a list containing N by N matrices. Each item in the list has a name which corresponds to the date for the matrix.

Author(s)

Scott Payseur, Onno Kleen, and Emil Sjoerup.

References

Barndorff-Nielsen, O. E., Hansen, P. R., Lunde, A., and Shephard, N. (2008). Designing realized kernels to measure the ex post variation of equity prices in the presence of noise. Econometrica, 76, 1481-1536.

Hansen, P. and Lunde, A. (2006). Realized variance and market microstructure noise. Journal of Business and Economic Statistics, 24, 127-218.

Zhou., B. (1996). High-frequency data and volatility in foreign-exchange rates. Journal of Business & Economic Statistics, 14, 45-52.

See Also

ICov for a list of implemented estimators of the integrated covariance.

Examples

# Univariate:
rvKernel <- rKernelCov(rData = sampleTData[, list(DT, PRICE)], alignBy = "minutes",
                       alignPeriod = 5, makeReturns = TRUE)
rvKernel

# Multivariate:
rcKernel <- rKernelCov(rData = sampleOneMinuteData, makeReturns = TRUE)
rcKernel

jonathancornelissen/highfrequency documentation built on Jan. 10, 2023, 7:29 p.m.