CurVol: Curve Data Volatility Analysis

Description Usage Arguments Details Value References See Also Examples

var.forecast function forecasts the daily VaR and intra-day VaR curves according to intra-day return curves.

1	var.forecast(yd, sigma_pred, error_fit, quantile_v, Method)

`yd`	A (grid_point) x (number of observations) matrix drawn from N functional curves.
`sigma_pred`	The predicted conditional standard deviation curve obtained by using the functional ARCH/GARCH model.
`error_fit`	The residual obtained from the functional ARCH/GARCH model.
`quantile_v`	The percentile of the VaR forecasts.
`Method`	A string to indicate which method will be implemented to estimate the quantile of the error: "normal" - assuming errors following a normal distribution; "bootstrap" - bootstrapping the empirical distribution from the historical data; "evt" - fitting the error with a generalized Pareto distribution.

This function uses a two-step approach to forecast intra-day Value-at-Risk, in formula that
VaR_{i+1}^τ(t)=\hat{σ}_{i+1}(t)\hat{\varepsilon}^τ(t), for 1≤q i ≤q N, t\in[0,1], and the percentile τ \in [0,1],
where the forecats of conditional standard deviation \hat{σ}_{i+1}(t) can be obtained by using est.fArch, est.fGarch, or est.fGarchx. Note that when t=1, VaR_{i+1}^τ(1) is the forecast of daily VaR.

List of objects:

day_VaR: the daily VaR.

day_ES: the daily expected shortfall.

intraday_VaR: the intra-day VaR curves.

vio_seq: the violation curve for the intra-day VaR curves.

Rice, G., Wirjanto, T., Zhao, Y. (2020). Forecasting Value at Risk via intra-day return curves. International Journal of Forecasting. <doi:10.1016/j.ijforecast.2019.10.006>.

basis.est est.fGarch diagnostic.fGarch var.backtest var.vio

## Not run: 
# generate discrete evaluations of the FGARCH(1,1) process.
grid_point = 50; N = 200
yd = dgp.fgarch(grid_point, N, "garch")
yd = yd$garch_mat

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

# fit the curve data and the conditional volatility by using an FGARCH(1,1) model with M=1.
fd = fda::Data2fd(argvals=seq(0,1,len=50),y=yd,fda::create.bspline.basis(nbasis=32))
garch11_est = est.fGarch(fd, basis_est[,1])
diag_garch = diagnostic.fGarch(garch11_est, basis_est[,1], yd)

# get the in-sample fitted conditional variance and error.
sigma_fit = diag_garch$sigma2[,1:N]
error_fit = diag_garch$eps

# get in-sample intra-day VaR curve by assuming a point-wisely Gaussian distributed error term.
var_obj = var.forecast(yd, sigma_fit, error_fit, quantile_v=0.01, Method="normal")

# the intra-day VaR curves.
var_obj$intraday_VaR

## End(Not run)