Title: | Statistical Performance Measures to Evaluate Covariance Matrix Estimates |
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Description: | Statistical performance measures used in the econometric literature to evaluate conditional covariance/correlation matrix estimates (MSE, MAE, Euclidean distance, Frobenius distance, Stein distance, asymmetric loss function, eigenvalue loss function and the loss function defined in Eq. (4.6) of Engle et al. (2016) <doi:10.2139/ssrn.2814555>). Additionally, compute Eq. (3.1) and (4.2) of Li et al. (2016) <doi:10.1080/07350015.2015.1092975> to compare the factor loading matrix. The statistical performance measures implemented have been previously used in, for instance, Laurent et al. (2012) <doi:10.1002/jae.1248>, Amendola et al. (2015) <doi:10.1002/for.2322> and Becker et al. (2015) <doi:10.1016/j.ijforecast.2013.11.007>. |
Authors: | Carlos Trucios |
Maintainer: | Carlos Trucios <[email protected]> |
License: | GPL (>= 2) |
Version: | 0.1.0 |
Built: | 2025-03-08 04:15:17 UTC |
Source: | https://github.com/cran/StatPerMeCo |
Compute the asymmetric loss function between the matrices S and H. See, Laurent et al. (2012) and Amendola et al. (2015).
Asymm(S, H, b = 3)
Asymm(S, H, b = 3)
S |
Proxy for the conditional covariance/correlation matrix |
H |
Estimate of the conditional covariance/correlation matrix. |
b |
Degree of homogeneity. By default b=3 |
Carlos Trucios
Amendola, A., & Storti, G. (2015). Model uncertainty and forecast combination in high-dimensional multivariate volatility prediction. Journal of Forecasting, 34(2), 83-91.
Laurent, S., Rombouts, J. V., & Violante, F. (2012). On the forecasting accuracy of multivariate GARCH models. Journal of Applied Econometrics, 27(6), 934-955.
X = matrix(rnorm(4000),ncol=4) S = diag(4) H = cov(X) Asymm(S,H,b=3)
X = matrix(rnorm(4000),ncol=4) S = diag(4) H = cov(X) Asymm(S,H,b=3)
Compute the distance measure defined in Eq. (3.1) of Li et al. (2016) to compare the factor loading matrix in its Monte Carlos experiments.
dM1(A, Ahat)
dM1(A, Ahat)
A |
The original factor loading matrix A |
Ahat |
The estimated factor loading matrix A |
Carlos Trucios
Li, W., Gao, J., Li, K., & Yao, Q. (2016). Modeling Multivariate Volatilities via Latent Common Factors. Journal of Business & Economic Statistics, 34(4), 564-573.
Compute the discrepancy measure defined in Eq. (4.2) of Li et al. (2016) to compare the factor loading matrix in its Monte Carlos experiments.
dMA(A,Ahat,y)
dMA(A,Ahat,y)
A |
The original factor loading matrix A |
Ahat |
The estimated factor loading matrix A |
y |
Matrix of observed returns |
Carlos Trucios
Li, W., Gao, J., Li, K., & Yao, Q. (2016). Modeling Multivariate Volatilities via Latent Common Factors. Journal of Business & Economic Statistics, 34(4), 564-573.
Compute the Frobenius distance between the matrices S and H. See, Laurent et al. (2012) and Amendola et al. (2015).
Frobenius(S, H)
Frobenius(S, H)
S |
Proxy for the conditional covariance/correlation matrix |
H |
Estimate of the conditional covariance/correlation matrix. |
Carlos Trucios
Amendola, A., & Storti, G. (2015). Model uncertainty and forecast combination in high-dimensional multivariate volatility prediction. Journal of Forecasting, 34(2), 83-91.
Laurent, S., Rombouts, J. V., & Violante, F. (2012). On the forecasting accuracy of multivariate GARCH models. Journal of Applied Econometrics, 27(6), 934-955.
X = matrix(rnorm(4000),ncol=4) S = diag(4) H = cov(X) Frobenius(S, H)
X = matrix(rnorm(4000),ncol=4) S = diag(4) H = cov(X) Frobenius(S, H)
Compute the Euclidean distance between the matrices S and H. See, Laurent et al. (2012) and Amendola et al. (2015).
LE(S, H)
LE(S, H)
S |
Proxy for the conditional covariance/correlation matrix |
H |
Estimate of the conditional covariance/correlation matrix. |
Carlos Trucios
Amendola, A., & Storti, G. (2015). Model uncertainty and forecast combination in high-dimensional multivariate volatility prediction. Journal of Forecasting, 34(2), 83-91.
Laurent, S., Rombouts, J. V., & Violante, F. (2012). On the forecasting accuracy of multivariate GARCH models. Journal of Applied Econometrics, 27(6), 934-955.
X = matrix(rnorm(4000),ncol=4) S = diag(4) H = cov(X) LE(S, H)
X = matrix(rnorm(4000),ncol=4) S = diag(4) H = cov(X) LE(S, H)
Compute the Eigenvalue loss function between the matrices S and H. See, Amendola et al. (2015).
Leig(S, H)
Leig(S, H)
S |
Proxy for the conditional covariance/correlation matrix |
H |
Estimate of the conditional covariance/correlation matrix. |
Carlos Trucios
Amendola, A., & Storti, G. (2015). Model uncertainty and forecast combination in high-dimensional multivariate volatility prediction. Journal of Forecasting, 34(2), 83-91.
X = matrix(rnorm(4000),ncol=4) S = diag(4) H = cov(X) Leig(S, H)
X = matrix(rnorm(4000),ncol=4) S = diag(4) H = cov(X) Leig(S, H)
Compute the Elw loss function between the matrices S and H. See, Engle et al. (2016).
Elw (Engle - Ledoit - Wolf) loss function is defined in Equation (4.6) of Engle et al. (2016).
Lelw(S, H)
Lelw(S, H)
S |
Proxy for the conditional covariance/correlation matrix |
H |
Estimate of the conditional covariance/correlation matrix. |
Carlos Trucios
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.
X = matrix(rnorm(4000),ncol=4) S = diag(4) H = cov(X) Lelw(S, H)
X = matrix(rnorm(4000),ncol=4) S = diag(4) H = cov(X) Lelw(S, H)
Compute the Mean Absolute Error between the matrices S and H. See, Becker et al.(2015).
MAE(S, H)
MAE(S, H)
S |
Proxy for the conditional covariance/correlation matrix |
H |
Estimate of the conditional covariance/correlation matrix. |
Carlos Trucios
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.
X = matrix(rnorm(4000),ncol=4) S = diag(4) H = cov(X) MAE(S, H)
X = matrix(rnorm(4000),ncol=4) S = diag(4) H = cov(X) MAE(S, H)
Compute the Mean Square Error between the matrices S and H. See, Becker et al. (2015).
MSE(S, H)
MSE(S, H)
S |
Proxy for the conditional covariance/correlation matrix |
H |
Estimate of the conditional covariance/correlation matrix. |
Carlos Trucios
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.
X = matrix(rnorm(4000),ncol=4) S = diag(4) H = cov(X) MSE(S, H)
X = matrix(rnorm(4000),ncol=4) S = diag(4) H = cov(X) MSE(S, H)
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)
StatPerMeas(S, H, measure , b)
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) |
Carlos Trucios
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.
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)
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)
Compute the Stein loss function between the matrices S and H. See, Laurent et al. (2012).
Stein(S, H)
Stein(S, H)
S |
Proxy for the conditional covariance/correlation matrix |
H |
Estimate of the conditional covariance/correlation matrix. |
Carlos Trucios
Laurent, S., Rombouts, J. V., & Violante, F. (2012). On the forecasting accuracy of multivariate GARCH models. Journal of Applied Econometrics, 27(6), 934-955.
X = matrix(rnorm(4000),ncol=4) S = diag(4) H = cov(X) Stein(S, H)
X = matrix(rnorm(4000),ncol=4) S = diag(4) H = cov(X) Stein(S, H)