ReMeDI {highfrequency}

ReMeDI

Description

This function estimates the auto-covariance of market-microstructure noise

Let the observed price Y_{t} be given as Y_{t} = X_{t} + \varepsilon_{t}, where X_{t} is the efficient price and \varepsilon_t is the market microstructure noise

The estimator of the l'th lag of the market microstructure is defined as:

\hat{R}^{n}_{t,l} = \frac{1}{n_{t}} \sum_{i=2k_{n}}^{n_{t}-k_{n}-l} \left(Y_{i+l}^n - Y_{i+l+k_{n}}^{n} \right) \left(Y_{i}^n - Y_{i- 2k_{n}}^{n} \right),

where k_{n} is a tuning parameter. In the function knChooseReMeDI, we provide a function to estimate the optimal k_{n} parameter.

Usage

ReMeDI(pData, kn = 1, lags = 1, makeCorrelation = FALSE)

Arguments

pData

xts or data.table containing the log-prices of the asset

kn

numeric of length 1 determining the tuning parameter kn this controls the lengths of the non-overlapping interval in the ReMeDI estimation

lags

numeric containing integer values indicating the lags for which to estimate the (co)variance

makeCorrelation

logical indicating whether to transform the autocovariances into autocorrelations. The estimate of variance is imprecise and thus, constructing the correlation like this may show correlations that fall outside (-1,1).

Note

We Thank Merrick Li for contributing his Matlab code for this estimator.

Author(s)

Emil Sjoerup.

References

Li, M. and Linton, O. (2021). A ReMeDI for microstructure noise. Econometrica, forthcoming

Examples

remed <- ReMeDI(sampleTData[as.Date(DT) == "2018-01-02", ], kn = 2, lags = 1:8)
# We can also use the algorithm for choosing the kn tuning parameter
optimalKn <- knChooseReMeDI(sampleTData[as.Date(DT) == "2018-01-02",],
                            knMax = 10, tol = 0.05, size = 3,
                            lower = 2, upper = 5, plot = TRUE)
optimalKn
remed <- ReMeDI(sampleTData[as.Date(DT) == "2018-01-02", ], kn = optimalKn, lags = 1:8)