Time-varying Variance-Covariance Estimation

Source: R/tvCov.R

Estimation of a time-varying variance-covariance matrix using the local constant or the local linear kernel smoothing methodologies.

tvCov(
  x,
  bw = NULL,
  cv.block = 0,
  est = c("lc", "ll"),
  tkernel = c("Triweight", "Epa", "Gaussian")
)

Arguments

x

A matrix.
bw

A scalar.
cv.block

A positive scalar with the size of the block in leave-one block-out cross-validation. By default 'cv.block=0' meaning leave-one-out cross-validation.
est

A character, either "lc" or "ll" for local constant or local linear.
tkernel

A character, either "Triweight, "Epa" or "Gaussian" kernel functions.

Value

A matrix of dimension obs x neq x neq.

References

Aslanidis, N. and Casas, I (2013) Nonparametric correlation models for portfolio allocation. Journal of Banking \& Finance, 37, 2268-2283

See also

bwCov

Examples

##Generate two independent (uncorrelated series)
y <- cbind(rnorm(100, sd = 4), rnorm(100, sd = 1))

##Estimation variance-variance matrix. If the bandwidth is unknown, it can
##calculated with function bwCov()
Sigma.hat <-  tvCov(y, bw = 1.4)

##The first time estimate
print(Sigma.hat[,,1])

#>           [,1]      [,2]
#> [1,] 15.382965 -1.175845
#> [2,] -1.175845  1.033527
##The mean over time of all estimates
print(apply(Sigma.hat, 1:2, mean))

#>            [,1]       [,2]
#> [1,] 13.0650645 -0.8566088
#> [2,] -0.8566088  0.9647204
##Generate two dependent variables
y <- MASS::mvrnorm(n = 100, mu = c(0,0), Sigma = cbind(c(1, -0.5), c(-0.5, 4)))

##Estimation variance-variance matrix
Sigma.hat <-  tvCov(y, bw = 3.2)
##The first time estimate
print(Sigma.hat[,,1])

#>            [,1]       [,2]
#> [1,]  0.8223837 -0.2518741
#> [2,] -0.2518741  3.1337540