Séries Temporais - Lista 3
Aluno: Rafael Cabral Fernandez e João Victor Messa
Introdução
Este documento refere-se a lista 3 de exercÃcios proposta pela professora Sandra Canton, da cadeira de Séries Temporais, como cômputo de ensino da disciplina, para a turma do semestre de 2018.2
2
Simule um passeio aleatório com n = 300 observando e indicando a conclusão obtida na questão 1.
T=300
set.seed(9999999)
Var=36.2
w=rnorm(T, 0,Var)
phi=1
x <- rep(0, T)
x[1]<- w[1]
for (i in 2:T) {
x[i] = 5+ phi* x[i - 1] + w[i]
}
x=x[0:T]
plot(x,type="l",col="burlywood4",main="Passeio aleatório", xlab="Observações",ylab="y")
4
Utilize o programa do R para plotar os correlogramas teóricos dos modelos definidos em (3).
#a)AR(1) e phi = 0.7
AR1acf=ARMAacf(c(0.7),0, lag.max = 20, pacf = FALSE)
plot(AR1acf,ylim=range(-1,1),col="burlywood4",type="h",main="AR(1) e phi = 0.7");abline(h=0)
#b)AR(1) e phi = -0.6
AR1acf=ARMAacf(c(-0.6),0, lag.max = 20, pacf = FALSE)
plot(AR1acf,ylim=range(-1,1),col="burlywood4",type="h",main="AR(1) e phi = -0.6");abline(h=0)
#c)ARMA(1,1) com parâmetros 0,5 e -0,4
ARMA21acf=ARMAacf(0.5, -0.4, lag.max = 20, pacf =FALSE)
plot(ARMA21acf,col="burlywood4",type="h",ylim=range(-1,1),main="ARMA(1,1) com phi = 0.5 e theta = -0.4");abline(h=0)
#d) MA(2) paramelho escolha
MA1acf=ARMAacf(0,c(-0.5,1.8), lag.max = 10, pacf = FALSE)
plot(MA1acf,main="MA(2) e theta = -0.5 e 1.8",col="burlywood4",type="h");abline(h=0)
phi1=-0.5
phi2=1.8
zeros=polyroot(c(1,phi1,phi2))
zeros## [1] 0.1388889+0.7323015i 0.1388889-0.7323015imodulo=abs(zeros)
modulo## [1] 0.745356 0.745356#e) AR(2) paramelho escolha
MA1acf=ARMAacf(c(0.5,0.2),0, lag.max = 10, pacf = FALSE)
plot(MA1acf,col="burlywood4",type="h",main="AR(2) e phi = 0.5 e 0.2");abline(h=0)
phi1=0.5
phi2=0.2
zeros=polyroot(c(1,phi1,phi2))
zeros## [1] -1.25+1.85405i -1.25-1.85405imodulo=abs(zeros)
modulo## [1] 2.236068 2.236068#f) ARMA(3,1) paramelho escolha
ARMA21acf=ARMAacf(c(0.8,0.3,-0.3), 0.8, lag.max = 20, pacf =FALSE)
plot(ARMA21acf,col="burlywood4",type="h",ylim=range(-1,1),main="ARMA(3,1) com phi = 0.8, 0.3 e -0.3 e theta = 0.8");abline(h=0)
phi1=0.8
phi2=0.3
phi3=-0.3
zeros=polyroot(c(1,phi1,phi2,phi3))
zeros## [1] -0.7773131+0.8370225i -0.7773131-0.8370225i 2.5546262+0.0000000imodulo=abs(zeros)
modulo## [1] 1.142288 1.142288 2.5546265
Utilize o programa do R para plotar a função de autocorrelação e autocorrelação parcial teórica dos seguintes modelos: O que se observa em cada situação? Escolha os valores dos parâmetros dentro da região de admissibilidade usando o comando polyroot
par(mfrow=c(1,5))
AR1acf=ARMAacf(c(0.7),0, lag.max = 20, pacf = FALSE)
plot(AR1acf,ylim=range(-1,1),col="burlywood4",type="h",main="AR(1)");abline(h=0)
AR1acf=ARMAacf(c(0.5,0.4),0, lag.max = 20, pacf = FALSE)
plot(AR1acf,ylim=range(-1,1),col="burlywood4",type="h",main="AR(2)");abline(h=0)
AR1acf=ARMAacf(c(0.5,0.4,-0.2),0, lag.max = 20, pacf = FALSE)
plot(AR1acf,ylim=range(-1,1),col="burlywood4",type="h",main="AR(3)");abline(h=0)
AR1acf=ARMAacf(c(0.5,0.4,-0.2,0.2),0, lag.max = 20, pacf = FALSE)
plot(AR1acf,ylim=range(-1,1),col="burlywood4",type="h",main="AR(4)");abline(h=0)
AR1acf=ARMAacf(c(0.5,0.4,-0.2,0.2,-0.1),0, lag.max = 20, pacf = FALSE)
plot(AR1acf,ylim=range(-1,1),col="burlywood4",type="h",main="AR(5)");abline(h=0)
phi1=0.7
phi2=0.5
zeros=polyroot(c(1,phi1,phi2))
zeros## [1] -0.7+1.228821i -0.7-1.228821imodulo=abs(zeros)
modulo## [1] 1.414214 1.414214par(mfrow=c(1,5))
AR1acf=ARMAacf(0,c(0.7), lag.max = 20, pacf = FALSE)
plot(AR1acf,ylim=range(-1,1),col="burlywood4",type="h",main="MA(1)");abline(h=0)
AR1acf=ARMAacf(0,c(0.5,0.4), lag.max = 20, pacf = FALSE)
plot(AR1acf,ylim=range(-1,1),col="burlywood4",type="h",main="MA(2)");abline(h=0)
AR1acf=ARMAacf(0,c(0.5,0.4,-0.2), lag.max = 20, pacf = FALSE)
plot(AR1acf,ylim=range(-1,1),col="burlywood4",type="h",main="MA(3)");abline(h=0)
AR1acf=ARMAacf(0,c(0.5,0.4,-0.2,0.2), lag.max = 20, pacf = FALSE)
plot(AR1acf,ylim=range(-1,1),col="burlywood4",type="h",main="MA(4)");abline(h=0)
AR1acf=ARMAacf(0,c(0.5,0.4,-0.2,0.2,-0.1), lag.max = 20, pacf = FALSE)
plot(AR1acf,ylim=range(-1,1),col="burlywood4",type="h",main="MA(5)");abline(h=0)
6
x1=arima.sim(list(order = c(1,0,0), ar = 0.9), n = 1000)
ts.plot(x1,col="burlywood4",main="AR(1) e Phi = 0.9")
x2=arima.sim(list(order = c(1,0,0), ar = 0.1), n = 1000)
ts.plot(x2,col="burlywood4",main="AR(1) e Phi = 0.1")
x3=arima.sim(list(order = c(0,0,1), ma = -0.9), n = 1000)
ts.plot(x3,col="burlywood4",main="MA(1) e Theta = -0.9")
x4=arima.sim(list(order = c(0,0,1), ma = 0.2), n = 1000)
ts.plot(x4,col="burlywood4",main="MA(1) e Theta = 0.2")
x5=arima.sim(list(order = c(1,0,1),ar =-0.7 , ma = 0.1), n = 1000)
ts.plot(x5,col="burlywood4",main="ARMA(1,1) com Phi = -0.7 e Theta = 0.1")
x6=arima.sim(list(order = c(2,0,0), ar = c(0.5,0.4)), n = 1000)
ts.plot(x6,col="burlywood4",main="AR(2) e Phi = 0.5 e 0.4")
x7=arima.sim(list(order = c(0,0,2), ma = c(-0.5,1.8)), n = 1000)
ts.plot(x7,col="burlywood4",main="MA(2) e Theta = -0.5 e 1.8")