#panggil data
library(Rssa)
dat<- read.csv(file.choose(),sep = ",", header=TRUE)
data<-as.matrix(dat)
n<-length(data)
P<-3 # Periode Musiman Data,hasil pengujian
insample=data[1:(n-P-9)]
n1<-length(insample)
outsample=data[(n-P-9+1):n]
outsample
L=19 # Trial And error
K=n1-L+1
#1. DEKOMPOSISI
###EMBEDDING###
z=as.matrix(insample)
z
x=embed(z,L)
id=1:L
y=rbind(id,x)
y
w=as.matrix(y)
sort=w[,order(-w[1,])]
sort
THankel=as.matrix(sort[-1,(1:L)])
THankel
Hankel=t(THankel)
Hankel
dim(Hankel)
##SVD##
trajectory=Hankel%*%t(Hankel)
dim(trajectory)
#eigen value
e.value=eigen(trajectory)$values
e.value
#singular value
sing.value=sqrt(e.value)
sing.value
#eigen vector ##untuk penentuan grouping
e.vector=eigen(trajectory)$vectors
e.vector
#principal component
princip.comp=matrix(0,nrow=K,ncol=L)
V=(t(Hankel)%*%e.vector)
V
for (i in 1:L)
{
  princip.comp[,i]=V[,i]/sqrt(e.value[i])
}
V
# plot singular value
S=ssa(dat, L=L)
S
plot(S)
#plot eigen vector 1D
plot(S,type="vectors", plot.method="matplot", idx=1:L) #1:berapa mau dilihat
#plot eigen vector 2D
plot(S, type="paired", idx=1:(L-1)) #(1:L-1)
#2. REKONSTRUKSI
###GROUPING###
r=reconstruct(S,groups=list(trend=c(1,2,3,4),s1=c(13,14),s2=c(5,18,19),s3=c(12,15),s4=c(6,8,9,
                                                                                        10,16,17)),len=12)#ganti groupingnya
r
plot(wcor(S,groups=list(trend=c(1,2,3,4),s1=c(13,14),s2=c(5,18,19),s3=c(12,15),s4=c(6,8,9,10,1
                                                                                    6,17)),len=12))#ganti groupingnya
###DIAGONAL AVERAGING###
komponen=cbind(r$trend,r$s1,r$s2,r$s3,r$s4) #ganti banyak F sebanyak groupingnya
komponen
diagonal.averaging=rowSums(komponen)
diagonal.averaging
da=diagonal.averaging
# plot data asli dan diagonal averaging
library(ggplot2)
df1=data.frame(periode=seq(1,132,length=132),penumpang=dat,isin="data asli")
df2=data.frame(periode=seq(1,120,length=120),penumpang=da,isin="diagonal averaging")
df=rbind(df1,df2)
ggplot(df,aes(x=periode,y=penumpang,color=isin))+geom_line()
#Linear Recurent Formula (LRF)
lrr.coef=lrr(S,groups=list(trend=c(1,2,3,4),s1=c(13,14),s2=c(5,18,19),s3=c(12,15),s4=c(6,8,9,10,16,17)),len=12) #ganti groupingnya
lrr.coef=lrr.coef$trend+lrr.coef$s1+lrr.coef$s2+lrr.coef$s3+lrr.coef$s4
lrr.coef
###RECURRENT FORECASTING###
forecast=rforecast(S,groups=list(trend=c(1,2,3,4),s1=c(13,14),s2=c(5,18,19),s3=c(12,15),s4=c(6,8,9,10,16,17)),len=10)
forecast
hasil.forecast=forecast$trend+forecast$s1+forecast$s2+forecast$s3+forecast$s4
hasil.forecast
##AKURASI PERAMALAN
residu=outsample-hasil.forecast
residu
MAD=(sum(abs(residu))/(length(outsample)))
MAD
MSE=(sum(residu^2)/(length(outsample)))
MSE
PEI=(residu/outsample)*100
MAPE=(sum(abs(PEI)))/(length(outsample))
MAPE
## Tracking Signal
ts=c()
for (i in 1:12){
  TS =sum(residu[1:i])/(sum(abs(residu[1:i]))/i)
  ts=c(ts,TS)
}
ts