#' classic grey forecasting model, GM(1,1)
#'
#' model sequential data with GM(1,1) model
#' @export
#' @examples
#' g<-gm(y)
#' @param x data sequence.
#' @param term length of extropotation data, forecasting data.
#' @param bg background formula.
#' @param buff buffer operator used for original data.
#' @param alpha coefficient of buffer operator if used.
gm<-function(y,ntest=NULL,term=1,bg=background,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) #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)
#p=LSE(x0[2:n],-bg(x1),ones(n-1))
p=lm(x0[2:n]~I(-bg(x1)))$coefficients
names(p)=c('b','a')
##--生成响应式序列ftd_x0和ftd_x1
trf_x0=function(k) ((x0[1]-p['b']/p['a'])*(1-exp(p['a']))*exp(-p['a']*(k-1)))
fitted_x0<-trf_x0(1:n)
fitted_x0[1]<-x0[1]
names(fitted_x0)<-names(x)
forecasts<-trf_x0((n+1):nf)
names(forecasts)<-as.numeric(names(x0)[n])+1:term
obj<-list(
data = x,
test = test,
parameter = data.frame(a=p['a'],b=p['b'],ax=0.5),
fitted = fitted_x0[1:n],
term = term,
forecasts = forecasts,
mape.in = mape(x0,fitted_x0),
mape.out = ifelse(is.null(ntest), NA, mape(test,forecasts[1:ntest])),
method = list(name="GM(1,1)",class="gm",mdname="GM(1,1)",buff=buff,alpha=alpha)
)
class(obj)<-"greyforecasting"
obj
}
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