%%%%% Supponiamo di avere la traccia "traccia1.txt",
%%%%% di cui ci viene dichiarato il tempo: 10 valori al secondo.
%%%%% Costruiamo alcuni modelli.

x.emp<-read.table(file="traccia.txt")
x.emp<-x.emp[,1]

ts.plot(x.emp)

hist(x.emp,50)

qqnorm(x.emp)

%%%%% MODELLO BANALE

m<-mean(x.emp)
s<-sd(x.emp)
L<-length(x.emp)
x.sint<-rnorm(L,m,s)
ts.plot(x.sint)


plot(c(1,100),c(-6,6))
lines(x.emp+3)
lines(x.sint-3,col="red")

%%%%% MODELLO A TEMPO DISCRETO

acf(x.emp, 100)

L<-length(x.emp)
X4<-x.emp[1:(L-4)]
X3<-x.emp[2:(L-3)]
X2<-x.emp[3:(L-2)]
X1<-x.emp[4:(L-1)]
Y  <-x.emp[5:L]
REG <- lm(Y~X1+X2+X3+X4)
summary(REG)


L<-length(x.emp)
X1<-x.emp[1:(L-1)]
Y  <-x.emp[2:L]
REG <- lm(Y~X1)
summary(REG)


b<-REG$coefficients[1]
a1<-REG$coefficients[2]

W<-rnorm(L,0,1)
x.sint<-1:L
x.sint[1]<-x.emp[1]
for (n in 2:L) {
x.sint[n] <- a1*x.sint[n-1] + b + 0.969*W[n]
}
plot(c(1,100),c(-6,6))
lines(x.emp+3)
lines(x.sint-3,col="red")

%%%%%  PREVISIONE

X1<-x.emp[1:(500-1)]
Y  <-x.emp[2:500]
REG.new <- lm(Y~X1)
summary(REG.new)


b<-REG.new$coefficients[1]
a1<-REG.new$coefficients[2]

P<-1:L
P[1:500]<-x.emp[1:500]
for (n in 1:(L-500)) {
P[500+n]<-a1*x.emp[500+n-1]+b
}

ts.plot(x.emp[501:L])
lines(P[501:L],col="red")

ts.plot(x.emp[501:600])
lines(P[501:600],col="red")