FOLD Instruction

FOLD( options ) cseries start end newcseries newstart

FOLD computes an implied spectral density function for a lower sampling rate. For instance, it takes a spectrum based on monthly data and computes the spectrum you would observe if data were only available quarterly.

Parameters

cseries	source series
start, end	range to transform, by default, range of cseries
newcseries	result series. Must be different from cseries
newcstart	start for newcseries, by default, start

Options

FACTOR=reduction factor [1]

The ratio of sampling rates, for instance 3=(12/4) for monthly to quarterly. FOLD transforms N frequencies to (N/reduction factor frequencies).

Description

FOLD sets each frequency in newcseries equal to the sum of all the frequencies for cseries aliased with it at the lower sampling rate.

Example

* nords is the number of ordinates,

* nobs is the number of actual data points

compute nords=768

freq 5 nords

rtoc 1966:1 2017:11

# ipx

# 1

compute nobs=%nobs

fft 1

cmult(scale=1./(2*%pi*nobs)) 1 1

fold(factor=3) 1 1 nords 2

Series 2 has 768/3=256 entries, which are entries 1+257+513, 2+258+514,... of series 1.