gof_fGARCH {FTSgof} | R Documentation |
Goodness-of-fit Test for Functional ARCH/GARCH Model
Description
It tests the goodness-of-fit of functional ARCH/GARCH models by accounting for the effect of functional GARCH parameter estimation.
Usage
gof_fGARCH(f_data, M, model, H = 10, pplot = NULL, max_eval = 10000)
Arguments
f_data |
A |
M |
A positive integer specifying the number of basis functions. |
model |
A string to indicate which model will be estimated: "arch" - FARCH(1); "garch" - FGARCH(1,1). |
H |
A positive integer specifying the maximum lag for which test statistics are computed. |
pplot |
A Boolean value. If TRUE, the function will produce a plot of p-values of the test
as a function of maximum lag |
max_eval |
The maximum number of evaluations of the optimization function, used in the "arch" and "garch" tests. |
Details
It tests the goodness-of-fit of the fARCH(1) or fGARCH(1,1) models.
It fits the model to the input data and applies the test M_{N,H}
in fport_wn
to the model residuals.
The asymptotic distribution is adjusted to account for the estimation effect,
because the model residual depends on the joint asymptotics of the innovation process and
the estimated parameters. We assume that the kernel parameters are consistently estimated
by the Least Squares method proposed in Aue et al. (2017).
Then, the asymptotic distribution of the statistic M_{N,H}
is given in Theorem 3.1
in Rice et al. (2020).
Value
p-value.
References
[1] 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>.
[2] Rice, G., Wirjanto, T., Zhao, Y. (2020). Tests for conditional heteroscedasticity of functional data. Journal of Time Series Analysis. 41(6), 733-758. <doi:10.1111/jtsa.12532>.
Examples
# generate discrete evaluations of the FGARCH process.
set.seed(42)
yd = dgp.fgarch(J=50, N=200, type = "garch")$garch_mat
# test the adequacy of the FARCH(1) model.
gof_fGARCH(yd, M=2, model = "arch", H=10, pplot=TRUE)