sigex.whichtrend <- function(mdl)
{
##########################################################################
#
# sigex.whichtrend
# Copyright (C) 2017 Tucker McElroy
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program. If not, see <https://www.gnu.org/licenses/>.
#
############################################################################
################# Documentation #####################################
#
# Purpose: determines which component (index) corresponds to trend
# Background:
# A sigex model consists of process x = sum y, for
# stochastic components y. Each component process y_t
# is either stationary or is reduced to stationarity by
# application of a differencing polynomial delta(B), i.e.
# w_t = delta(B) y_t is stationary.
# These differencing polynomials must be relatively prime.
# (This is an assumption of the code.) If delta(1) = 0,
# then there is at least one unit root of that component,
# and hence that component corresponds to the stochastic trend.
# (It could have other non-stationary effects as well, but it
# at least contains some unit roots, and hence is designated
# as the trend component.)
# Inputs:
# mdl: the specified sigex model, a list object.
# mdl[[1]] is mdlK, gives ranks of white noise covariance matrix
# mdl[[2]] is mdlType, a list giving t.s. model class, order, and bounds
# mdl[[3]] is mdlDiff, gives delta differencing polynomials
# mdl[[4]] is list of regressors by individual series
# Outputs:
# trendcomp: index of the latent component that has a stochastic trend
#
####################################################################
numcomp <- length(mdl[[3]])
trendcomp <- NULL
for(i in 1:numcomp)
{
if(sum(mdl[[3]][[i]])==0) trendcomp <- i
}
return(trendcomp)
}
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