time_varying_cov: Estimate Time-Varying Covariance Matrix Using Local PCA

In TVMVP: Time-Varying Minimum Variance Portfolio

Estimate Time-Varying Covariance Matrix Using Local PCA

Description

This function estimates a time-varying covariance matrix using local principal component analysis and the soft thresholding for residual shrinkage. By default, only the total covariance matrix is returned. Optionally, the user can retrieve all intermediate components of the estimation process. The procedure is available either as a stand-alone function or as a method in the 'TVMVP' R6 class.

Usage

time_varying_cov(
  obj,
  max_factors = 3,
  kernel_func = epanechnikov_kernel,
  M0 = 10,
  rho_grid = seq(0.005, 2, length.out = 30),
  floor_value = 1e-12,
  epsilon2 = 1e-06,
  full_output = FALSE
)

Arguments

obj	An object of class TVMVP with the data.
max_factors	The number of factors to use in local PCA.
kernel_func	The kernel function to use (default is epanechnikov_kernel).
M0	Integer. The number of observations to leave out between the two sub-samples in the adaptive thresholding procedure. Default is 10.
rho_grid	A numeric vector of candidate shrinkage parameters \rho used in adaptive_poet_rho. Default is seq(0.005, 2, length.out = 30).
floor_value	A small positive number specifying the lower bound for eigenvalues in the final positive semidefinite repair. Default is 1e-12.
epsilon2	A small positive tuning parameter for the adaptive thresholding. Default is 1e-6.
full_output	Logical; if TRUE, returns all components of the estimation.

Details

The function estimates a time-varying covariance matrix using Local PCA:

\hat{\Sigma}_{r,t}=\hat{\Lambda}_t \hat{\Sigma}_F \hat{\Lambda}_t' + \tilde{\Sigma}_e

Where \hat{\Lambda}_t is the factor loadings at time t, \hat{\Sigma}_F is the factor covariance matrix, and \tilde{\Sigma}_e is regularized covariance matrix of the idiosyncratic errors.

Two usage styles:

# Function interface
tv <- TVMVP$new()
tv$set_data(returns)
cov <- time_varying_cov(tv, m = 5)

# R6 method interface
tv$determine_factors(max_m = 5)
cov <- tv$time_varying_cov()

Value

By default, a covariance matrix. If full_output = TRUE, a list containing:

• total_cov – the estimated covariance matrix,

• residual_cov – the residual (idiosyncratic) covariance,

• loadings – estimated factor loadings,

• best_rho – optimal shrinkage parameter,

• naive_resid_cov – residual covariance before shrinkage

References

Lillrank, E. (2025). A Time-Varying Factor Approach to Covariance Estimation

Chen, J., Li, D., & Linton, O. (2019). A new semiparametric estimation approach for large dynamic covariance matrices with multiple conditioning variables. Journal of Econometrics, 212(1), 155–176.

Fan, Q., Wu, R., Yang, Y., & Zhong, W. (2024). Time-varying minimum variance portfolio. Journal of Econometrics, 239(2), 105339.

Examples

set.seed(123)
returns <- matrix(rnorm(100 * 30), nrow = 100, ncol = 30)

# Initialize object
tv <- TVMVP$new()
tv$set_data(returns)

# Using function interface
time_varying_cov(obj = tv, m = 3)

# Or using R6 method
tv$time_varying_cov(m=3)

TVMVP documentation built on June 28, 2025, 1:08 a.m.