XploRe Help : npgarchest

Keywords - Function groups - @ A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

Library:	times
See also:	genarma genarch nparmaest

Quantlet:		npgarchest
Description:		fits a nonparametric GARCH(1,1) process e[t+1] = s[t+1]*Z[t+1], s[t+1]^2 = g(e[t]^2,s[t]^2), where Z[t] are iid Gaussian, by inverting deconvolution kernel estimators.

Reference(s):

Holzberger, H. (2001). PhD Thesis, Uni Kaiserslautern Franke, J., Holzberger, H. and Mueller, M. (2001). Nonparametric Estimators of GARCH Processes, in Haerdle, Kleinow, Stahl (eds.): Applied Quantitative Finance.

Usage:	`npfit = npgarchest(y, {h1 {,h2 {,N {,R {,debug}}}}})`
Input:
	`y`	n x 1 vector, time series.
	`h1`	optional scalar, bandwidth for univariate density. (If h1 <= 0 or not given, it is set to standard deviation of 4/log(n))
	`h2`	optional 2 x 1 vector, bandwidth for bivariate density. (If h2 <= 0 or not given, it is set to standard deviation of (10/log(n))\|(8*n^0.2))
	`N`	optional positive scalar, number of grid points for the approximation of the nonparametric function. (Default is 50)
	`R`	optional positive scalar, number of grid points for internal approximations. (Default is 250)
	`debug`	optional scalar, should be set to 1 for plots during computation. (Default is 0.)
Output:
	`npfit.g`	N*N x 3 matrix, estimated function.
	`npfit.f`	N*N x 3 matrix, estimated function of the corresponding ARMA model.
	`npfit.d1`	R x 2 matrix, estimated one-dimensional deconvolution density estimator of the corresponding ARMA model.
	`npfit.d2`	N*N x 3 matrix, estimated two-dimensional combined deconvolution/regular density estimator.

Example:

library("times") library("kernel") {e,s2}=genarch(0.1|0.4,0.4,500) g=npgarchest(e) plot(setmask(g,"surface"))

Result:

Plot of the nonparametric bivariate function g.

Author: M. Mueller, 20020412