循环AR模型

Question

我想用一个有差分时间序列的AR(4)模型做一个n步的预测。

模型本身：

X(t)-X(t-1)=a(1)(X(t-1)-X(t-2))+...+a(4)(X(t-4)-X(t-5))

=> X(t)=X(t-1)+a(1)(X(t-1)-X(t-2))+...+a(4)(X(t-4)-X(t-5))

首次预测：

X(t+1)-X(t)=a(1)(X(t)-X(t-1))+...+a(4)(X(t-3)-X(t-4))

=> X(t+1)=X(t)+a(1)(X(t)-X(t-1))+...+a(4)(X(t-3)-X(t-4))

第二次预报：

X(t+2)-X(t+1)=a(1)(X(t+1)-X(t))+...+a(4)(X(t-2)-X(t-3))

=> X(t+2)=X(t+1)+a(1)(X(t+1)-X(t))+...+a(4)(X(t-2)-X(t-3))

我已经用这个代码试过了

N<-50
arkoef<-0
ar<-0
ARforecast<-numeric(0)
arkoef<-c(closingkursu[2518],closingkursu[2517],closingkursu[2516],closingkursu[2515],closingkursu[2514])
ar<-arkoef
for(i in 1:N){
ARforecast<-c(ARforecast,arkoef[1]+arfit$coef[1]*(arkoef[1]-arkoef[2])+arfit$coef[2]*(arkoef[2]-arkoef[3])+arfit$coef[3]*(arkoef[3]-arkoef[4])+arfit$coef[4]*(arkoef[4]-arkoef[5]))
ar = c(tail(ARforecast, 1), head(ar, -1))}

此代码的输出是：

ar1      ar1      ar1      ar1      ar1      ar1      ar1      ar1      ar1      ar1      ar1      ar1      ar1      ar1      ar1      ar1      ar1      ar1      ar1      ar1 
10.19656 10.19656 10.19656 10.19656 10.19656 10.19656 10.19656 10.19656 10.19656 10.19656 10.19656 10.19656 10.19656 10.19656 10.19656 10.19656 10.19656 10.19656 10.19656 10.19656 
     ar1      ar1      ar1      ar1      ar1      ar1      ar1      ar1      ar1      ar1      ar1      ar1      ar1      ar1      ar1      ar1      ar1      ar1      ar1      ar1 
10.19656 10.19656 10.19656 10.19656 10.19656 10.19656 10.19656 10.19656 10.19656 10.19656 10.19656 10.19656 10.19656 10.19656 10.19656 10.19656 10.19656 10.19656 10.19656 10.19656 
     ar1      ar1      ar1      ar1      ar1      ar1      ar1      ar1      ar1      ar1 
10.19656 10.19656 10.19656 10.19656 10.19656 10.19656 10.19656 10.19656 10.19656 10.19656 

第一个预测似乎是正确的，但循环不起作用。

Answer 1

您忘记在循环中增加ARforecast向量的值。

N<-50 ;  arkoef<-0  ;  ar<-0 ;  ARforecast<-numeric(0)
arkoef <- c(closingkursu[2518],closingkursu[2517],closingkursu[2516],closingkursu[2515],closingkursu[2514])
ar <- arkoef

for(i in 1:N){
  ARforecast[i+1] <- c(ARforecast[i], arkoef[i]+arfit$coef[i]*(arkoef[i]-arkoef[i+1])+arfit$coef[i+1]*(arkoef[i+1]-arkoef[i+2])+arfit$coef[i+2]*(arkoef[i+2]-arkoef[i+3])+arfit$coef[i+3]*(arkoef[i+3]-arkoef[i+4]))
  ar = c(tail(ARforecast, 1), head(ar, -1))
}

但我实际上并不理解代码的某些部分( ar在循环中做什么?)