StatPerMeas function

Statistical performance measures to evaluate conditional covariance matrix estimates.

Compute several statistical performance measures frequently used in the econometric literature to evaluate covariance/correlation matrix estimates. See, Laurent et al. (2012), Amendola et al. (2015), Becker et al. (2015) and Engle et al. (2016).

If measure="ALL" compute the Asymmetric loss function, Frobenius distance, Euclidean distance, Eigenvalue loss function, Mean Absolute Error, Mean Square Error, Stein loss function and Elw loss function.

StatPerMeas(S, H, measure , b)

Arguments

• S: Proxy for the conditional covariance/correlation matrix
• H: Estimate of the conditional covariance/correlation matrix.
• measure: "Le": Euclidean distance, "MSE": Mean Square Error, "MAE": Mean Absolute Error, "Lf": Frobenius distance, "Ls": Stein loss function, "Asymm": Asymmetric loss functions, "Leig": Eigenvalue loss function, "Lelw": Elw loss function, "ALL": All Statistical Performance Measures.
• b: Degree of homogeneity. By default b=3 (Used in the Frobenius distance)

References

Amendola, A., & Storti, G. (2015). Model uncertainty and forecast combination in high-dimensional multivariate volatility prediction. Journal of Forecasting, 34(2), 83-91.

Becker, R., Clements, A. E., Doolan, M. B., & Hurn, A. S. (2015). Selecting volatility forecasting models for portfolio allocation purposes. International Journal of Forecasting, 31(3), 849-861.

Laurent, S., Rombouts, J. V., & Violante, F. (2012). On the forecasting accuracy of multivariate GARCH models. Journal of Applied Econometrics, 27(6), 934-955.

Engle, Robert F. and Ledoit, Olivier and Wolf, Michael, Large dynamic covariance matrices (2016). University of Zurich, Department of Economics, Working Paper No. 231. Available at SSRN: https://ssrn.com/abstract=2814555.

Author(s)

Carlos Trucios

Examples

X = matrix(rnorm(4000),ncol=4)
S = diag(4)
H = cov(X)

StatPerMeas(S,H,measure="ALL",b=10)

StatPerMeas(S,H,measure=c("MSE","MAE","Ls"),b=4)