XploRe Help : nparmaest

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

Quantlet:		nparmaest
Description:		fits a nonparametric ARMA(1,1) process X[t+1] = f(X[t],e[t]) + e[t+1] 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 = nparmaest(x, {,h1 {,h2 {,N {,R {,debug}}}}})`
Input:
	`x`	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 * 3/log(n))
	`h2`	optional 2 x 1 vector, bandwidth for bivariate density. (If h2 <= 0 or not given, it is set to standard deviation * (5/log(n))\|(3*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.f`	N*N x 3 matrix, estimated function.
	`npfit.d1`	R x 2 matrix, estimated one-dimensional deconvolution density estimator.
	`npfit.d2`	N*N x 3 matrix, estimated two-dimensional combined deconvolution/regular density estimator.

Example:

library("times") library("kernel") x=genarma(0.8,0.8,normal(500)) f=nparmaest(x,0.8,1|2.3) plot(setmask(f,"surface"))

Result:

Plot of the nonparametric bivariate function f.

Author: M. Mueller, 20020412