CACCUMULATE Instruction

CACCUMULATE( options) cseries start end newcseries newcstart

Creates a running sum of a complex series: entry N of newcseries is the sum of the first N entries of cseries.

Parameters

cseries	source series
start, end	range to transform, by default, range of cseries
newcseries	result series, by default, overwrites cseries
newcstart	start for newcseries, by default, start

Options

STANDARDIZE/[NOSTANDARDIZE]

If you use STANDARDIZE, newcseries is normalized so it ends with 1.0. This option was known as SCALE before version 7.

Example

This is part of the @CUMPDGM procedure. The CACCUMULATE instruction cumulates the periodogram (squared Fourier transform) over frequencies 0 to \(pi\) and standardizes it to have an end value of 1.0. If the series examined is white noise, this cumulated periodogram should differ only slightly from the theoretical spectral distribution function for white noise: a straight line. The CXTREMUM instruction computes the maximum gap between the two distribution functions.

frequency 3 nords

compute half=(nords+1)/2

rtoc

# resids

# 1

clabels 1 2 3

# "Cumprdgm" "Whitenoise" "Gap"

fft 1

cmult 1 1 ;*Periodogram of resids

cacc(standardize) 1 1 half

cunits 2 ;*Spectral density of white noise (constant)

cacc(standardize) 2 1 half

csubtract 2 1 1 half 3

cxt(part=absval) 3 1 half ;*Computes extreme values of series 3