est.fGarch: Estimate Functional GARCH Model

In yzhao7322/CurVol: Curve Data Volatility Analysis

Description

est.fGarch function estimates the Functional GARCH(p,q) model by using the Quasi-Maximum Likelihood Estimation method.

Usage

est.fGarch(fdata, basis, p = 1, q = 1)

Arguments

fdata	The functional data object with N paths.
basis	The M-dimensional basis functions.
p	order of the depedence on past volatilities.
q	order of the depedence on past squared observations.

Value

List of model paramters:

d: d Parameter vector, for intercept function δ.

As: A Matrices, for α operators.

Bs: B Matrices, for β operators.

References

Aue, A., Horvath, L., F. Pellatt, D. (2017). Functional generalized autoregressive conditional heteroskedasticity. Journal of Time Series Analysis. 38(1), 3-21. <doi:10.1111/jtsa.12192>.
Cerovecki, C., Francq, C., Hormann, S., Zakoian, J. M. (2019). Functional GARCH models: The quasi-likelihood approach and its applications. Journal of Econometrics. 209(2), 353-375. <doi:10.1016/j.jeconom.2019.01.006>.

See Also

est.fArch est.fGarchx diagnostic.fGarch

Examples

## Not run: 
# generate discrete evaluations of the FGARCH process and smooth them into a functional data object.
yd = dgp.fgarch(grid_point=50, N=200, "garch")
yd = yd$garch_mat
fd = fda::Data2fd(argvals=seq(0,1,len=50),y=yd,fda::create.bspline.basis(nbasis=32))

# extract data-driven basis functions through the truncated FPCA method.
basis_est = basis.est(yd, M=2, "tfpca")$basis

# estimate an FGARCH(1,1) model with basis when M=1.
garch11_est = est.fGarch(fd, basis_est[,1])

## End(Not run)

yzhao7322/CurVol documentation built on Sept. 5, 2021, 8:41 p.m.