XploRe Help : parzen

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:	spec

Quantlet:		parzen
Description:		Calculates the parzen window. Parzen windows classification is a technique for nonparametric density estimation, which can also be used for classification. In the Parzen window (Parzen, 1961), for each frequency, the weights for the weighted moving average of the periodogram values are computed as: wj = 1-6(j/p)2 + 6(j/p)3 (for j = 0 to p/2) wj = 2*(1-j/p)3 (for j = p/2 + 1 to p) w-j = wj (for j <> 0)

Reference(s):

See e.g. M.B. Priestley (2000), Spectral Analysis and Time Series, Academic Press. E. Parzen (1992), Modern Probability Theory and Its Applications, Wiley&Sons.

Usage:	`w=parzen(x,t)`
Input:
	`x`	grid on which the function is calculated
	`t`	truncation point
Output:
	`w`	Parzen window

Note:

The "window" terminology arises from the fact that the weighting system determines what part of the periodogram is seen, i.e. has non-negligible weights, by the estimator. The width of the window, which is comparable to the class interval when constructing a histogram, is referred to as the bandwidth. It must be choosen with some care, since to small a bandwidth implies a large variance and too large a bandwidth may smooth out interesting features of the spectrum, such as peaks. The "Fast Fourier Transform" is a method of performing this calculation efficiently. (see Peter Kennedy, A Guide to Econometrics (19996), Blackwell Publishers)

Example:

library("times") parzen(0,9)

Result:

Contents of w
[1,]   6.75

Author: R. Chen, C. Hafner, W. Haerdle, G. Aydinli, 20010419 license MD*Tech