sigma_estim_ewma: EWMA Covariance Estimation

In antshi/CovEstim: (High-dimensional) Covariance Estimation

Description

Computes the Exponentially Moving Average (EWMA) estimator of the covariance matrix.

Usage

sigma_estim_ewma(data, lambda = 0.97)

Arguments

data	an nxp data matrix.
lambda	a double for the decay parameter λ. Default is 0.97 - the standard for monthly returns according to \insertCiteriskmetrics1996;textualCovEstim. If the data consists of daily returns, lambda should be set to 0.94.

Details

The EWMA estimator of the covariance matrix for an nxp data matrix X is computed with the following formula:

\hat{Σ}_{t}= (1-λ)R_{t}R'_{t} + λ\hat{Σ}_{t-1},

where R_{t} is the matrix of demeaned returns for the time period t and \hat{Σ}_{t-1} is the EWMA covariance estimator for the period t-1.

Value

a list with the following entries

• a pxp estimated covariance matrix.

• an estimation specific tuning parameter, here the decay parameter λ.

References

\insertAllCited

Examples

data(sp200)
sp_rets <- sp200[,-1]
sigma_ewma <- sigma_estim_ewma(sp_rets)[[1]]

antshi/CovEstim documentation built on Nov. 13, 2020, 2:25 p.m.