hohenTp<- read.table("C:/CLIM/HohenT.txt",header=T)          ###
attach(hohenTp)
 
#---------------------------------------------------------------
polypre<- function(Y,n,x1,x2,x3,x4,tst){            
polpr<- 1:(n+1)                               #vector of dim n+1
polpr[1:tst]<- mean(Y[1:tst])       
for (t in tst:n)
{poly<-lm(Y[1:t]~x1[1:t]+x2[1:t]+x3[1:t]+x4[1:t])
b<- poly$coefficients                        #$b vector of dim 5
t1<- t+1  
polpr[t1]<-b[1]+b[2]*x1[t1]+b[3]*x2[t1]+b[4]*x3[t1]+b[5]*x4[t1]  
}
return(polpr)                         
}

#----Preparing the input of function polypre--------------------
n<- length(Year); tst<- trunc(n/5); ts1<- tst+1
Y<-Tyear/100    
x1<- 1:(n+1)-n/2; x2<-x1*x1;  x3<-x2*x1; x4<-x2*x2 
          
Ypred<- polypre(Y,n,x1,x2,x3,x4,tst)  

"Poly_t-prediction last decade";  Ypred[(n-9):n]                
Ypre<- Ypred[ts1:n]; Yres<- Y[ts1:n]-Ypre; MSQ<- mean(Yres*Yres)
c("stdRes"=sqrt(var(Yres)), "MSQ"=MSQ,"rootMSQ"=sqrt(MSQ)) 
 
rm(list=objects())                                          ###