est.fArch | R Documentation |
est.fArch function estimates the Functional ARCH(q) model by using the Quasi-Maximum Likelihood Estimation method.
est.fArch(fdata, basis, q = 1)
fdata |
The functional data object with N paths. |
basis |
The M-dimensional basis functions. |
q |
The order of the depedence on past squared observations. If it is missing, q=1. |
This function estimates the Functional ARCH(q) model:
x_i(t)=\sigma_i(t)\varepsilon_i(t)
, for t \in [0,1]
and 1\leq i \leq N
,
\sigma_i^2(t)=\omega(t)+ \sum_{j=1}^q \int \alpha_j(t,s) x^2_{i-j}(s)ds
.
List of model paramters:
d: d Parameter vector, for intercept function \delta
.
As: A Matrices, for \alpha
operators.
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>.
Hormann, S., Horvath, L., Reeder, R. (2013). A functional version of the ARCH model. Econometric Theory. 29(2), 267-288. <doi:10.1017/S0266466612000345>.
est.fGarch
est.fGarchx
diagnostic.fGarch
## Not run:
# generate discrete evaluations of the FARCH process and smooth them into a functional data object.
yd = dgp.fgarch(grid_point=50, N=200, "arch")
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 FARCH(1) model with basis when M=1.
arch1_est = est.fArch(fd, basis_est[,1])
## End(Not run)
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