#' optimal gm model with background and response formula
#'
#' weighted background gm model and solved by auxillary parameters
#' @export
#' @param y data sequence.
#' @param present character vector containing xlab and ylab.
#' @param buff buffer operator used for original data.
#' @param alpha coefficient in buffer operator if used.
#' @examples
#' g<-gm_1(y,term=3)
gm_2 <- function(y,ntest=NULL,term=1,buff=NULL,alpha=NA){
#--原始数据截取ntest部分,生成建模序列x
if(is.null(names(y))) names(y)<-1:length(y)
if(is.numeric(ntest)){
x<-y[1:(length(y)-trunc(ntest))]
test<-y[(length(x)+1):length(y)]
}else{
x <- y
test <- NULL
}
ny=length(y) #原始序列长度
n=length(x) #x:建模序列长度
nf=n+term #拟合+预测序列长度
if(nf<ny){
stop("ntest is too small or term is too big")
}
##--缓冲处理,生成建模序列x0
if(is.function(buff)) {
if(is.na(alpha)) x0 <- buff(x) else x0 <- buff(x, alpha = alpha)
}else{
x0<-x
}
##--建模处理,生成参数向量p['a'],p['b']
x1=cumsum(x0)
auxillary=LSE(x0[2:n],-x1[2:n],ones(n-1))
a <- log(auxillary['a']+1)
ax <- 1/a -1/auxillary['a']
b <- auxillary['b']*a/auxillary['a']
##
fupper<- sum(exp(-a*(1:n))*x0[1:n])
flower<- sum(exp(-2*a*(1:n)))
belta<-fupper/flower
##
trf=function(k) belta*exp(-a*k)
fitted_x0<-trf(1:n)
fitted_x0[1]<-x0[1]
names(fitted_x0)<-names(x0)
forecasts<-trf(n+1:term)
names(forecasts)<-as.numeric(names(x0)[n])+1:term
obj<-list(
data =x,
test =test,
parameter =data.frame(a=a,b=b,ax=ax),
fitted =fitted_x0[1:n],
term =term,
forecasts =forecasts,
mape.in = mape(x0,fitted_x0[1:n]),
mape.out = ifelse(is.null(ntest), NA, mape(test,forecasts[1:ntest])),
method = list(name="Comprehensive Optimized GM(1,1) ",class="gm",mdname=" OBT-GM(1,1)",buff=buff,alpha=alpha)
)
class(obj)<-"greyforecasting"
obj
}
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