w1=rnorm(600,0,1)
w2=filter(w1,sides=2,rep(1,3)/3)
w3=vector(length=600)
for (i in 1:600)w3[i]=rnorm(1,0,i)
par(mfrow=c(3,1))
plot.ts(w1)
plot.ts(w2)
plot.ts(w3)
##################################################################
#Autoregresja x_n=x_(n-1)+0.9x_(n-2)+w_n
par(mfrow=c(1,1))
w4=filter(rnorm(650,0,1),filter=c(1,-.8),method="recursive")
plot.ts(w4[51:650])
##################################################################
#Błądzenie przypadkowe z dryfem i bez dryfu
#xn=0.1+x(n-1)+wn;wn-IID N(0,1)
set.seed(100)
w=rnorm(300,0,1);x=cumsum(w)
wd=w+.1;xd=cumsum(wd)
plot.ts(xd,ylim=c(-10,40))
lines(x)
lines(.1*(1:300),lty="dashed")
###################################################
# AR1s
set.seed(100)
x1=arima.sim(list(order=c(1,0,0), ar=.8), n=16000) 
acf(x1,lag.max =25)
plot(x1)
acf(x1)$acf

x2=arima.sim(list(order=c(1,0,0), ar=-.8), n=500)
plot(x2)
acf(x2,max.lag=25)

par(mfrow=c(2,1))
plot(x1,  main="AR1 phi = +.8")
plot(x2,  main="AR1 phi = -.8")
par(mfcol=c(2,2))
acf(x1, 20)
acf(x2, 20)
pacf(x1, 20)
pacf(x2, 20)

###################################################
# AR2
x=arima.sim(list(order=c(2,0,0), ar=c(1,-0.5)), n=50000) 
par(mfcol=c(3,1))
plot(x)
acf(x, 20)
pacf(x, 20)
par(mfrow=c(2,1))
acf(MA1,20,xlim=c(1,20))   
pacf(MA1,20,ylim=c(-.2,1)) 

###################################################
#MA(2)
set.seed(100)
a=arima.sim(list(order = c(0,0,2),ma=c(.8,.8)),n=100)
plot(a)
par(mfcol=c(2,1))
pacf(a,lag.max =40)
acf(a,lag.max =40)
acf(a)$acf
#**********************************************************
# ARMA(1,1)
x=arima.sim(list(order=c(1,0,1), ar=.8, ma=-.2), n=500)
par(mfcol=c(3,1))
plot(x)
acf(x, 30)
pacf(x, 30)
#**********************************************************
x = arima.sim(list(order=c(1,0,1), ar=.8, ma=-.2), n=500) 
(x.fit = arima(x, order = c(1, 0, 1))) #Remember: There is mean and not intercept
tsdiag(x.fit, gof.lag=20)
x.f=predict(x.fit, n.ahead=10)  
U = x.f$pred + 2*x.f$se
L = x.f$pred - 2*x.f$se
minx=min(x,L)
maxx=max(x,U)
par(mfcol=c(1,1))
ts.plot(x,x.f$pred,col=1:2, ylim=c(minx,maxx))
lines(U, col="blue", lty="dashed")
lines(L, col="blue", lty="dashed")