powerKernelBSSFit {BSS}R Documentation

Fitting power law kernel Brownian semistationary processes


powerKernelBSSFit uses a method of moments to fit the parameters of a power law kernel Brownian semistationary process to a vector of observations. A least squares estimate of the parameters is obtained by minimising the mean square error between the true power law kernel autocorrelation function (found by numerical intergration) and the empirical ACF of the data, using lags 0,...,H. The number of lags num_lags used can be adjusted. The volatility process does not need to be specified.


powerKernelBSSFit(Y, n, num_lags = 10)



a vector of observations of a BSS process at frequency n.


positive integer indicating the number of observations per unit of time.


the number of lags to be used in the regression. The default is to use the first 10 lags.


The function returns a list containing the parameters alpha and beta, and also the mean square error mse of the least squares fit. This can be used to compare model fit when trying different kernels.


N <- 10000
n <- 100
T <- 1.0
theta <- 0.5
beta_vol <- 0.125

kappa <- 3
alpha <- -0.2
beta_pwr <- -1.0

vol <- exponentiatedOrnsteinUhlenbeck(N, n, T, theta, beta_vol)
bss_simulation <- gammaKernelBSS(N, n, T, kappa, alpha, beta_pwr, sigma = vol)
y <- bss_simulation$bss

powerKernelBSSFit(y, n, num_lags = 10)

[Package BSS version 0.1.0 Index]