Bibliografia Principal

Exemplo 1(Shumway & Stoffer, 2016): Aquecimento global

library(astsa)
plot(globtemp, type="o", ylab="Global Temperature Deviations",col="darkblue")

Exemplo 2: PETR4 de 02-jan-2014 a 02-jul-2018

db_petr4=read.table("PETR4.csv", h=T, sep=",",dec=".")
r_petr4=diff(log(db_petr4$cotacao))
par(mfrow=c(3,1))
plot.ts(db_petr4$cotacao,col="darkblue")
plot.ts(r_petr4,col="darkblue")
plot.ts(r_petr4^2,col="darkblue")

Exemplo 3 (Morettin, P.A. e Toloi, C.M.C., 2004): Manchas solares

db_manchas=read.table("./ast-pam/manchas.csv", h=T, sep=",",dec=".")
plot.ts(db_manchas$manchas,col="darkblue")

Exemplo 4: Ruído branco

w = rnorm(2000,0,1)
plot.ts(w, main="Ruído Branco",col="darkblue")

Exemplo 5: Passeio aleatório

rw<-numeric()
rw[1] = rnorm(1,0,1)
for(t in 2:2000){
  rw[t]=rw[t-1]+rnorm(1,0,1)
}
plot.ts(rw, main="Passeio Aleatório",col="darkblue")

Exemplo 6 (Shumway & Stoffer, 2016): Passeio aleatório com tendência

set.seed(154)
 # so you can reproduce the results
w = rnorm(200); x = cumsum(w)
 # two commands in one line
wd = w +.2;
 xd = cumsum(wd)
plot.ts(xd, ylim=c(-5,55), main="random walk", ylab='')
lines(x, col=4); abline(h=0, col=4, lty=2); abline(a=0, b=.2, lty=2)

Exemplo 7 (Shumway & Stoffer, 2016, adaptado):

cs_l = 2*cos(2*pi*(1:500)/200 + .6*pi); w = rnorm(500,0,1)
cs = 2*cos(2*pi*1:500/50 + .6*pi); w = rnorm(500,0,1)
par(mfrow=c(3,2), mar=c(3,2,2,1), cex.main=1.5)
plot.ts(cs_l, main=expression(2*cos(2*pi*t/200+.6*pi)))
plot.ts(cs_l+cs+w, main=expression(2*cos(2*pi*t/200+.6*pi)+2*cos(2*pi*t/50+.6*pi) + N(0,1)))
plot.ts(cs, main=expression(2*cos(2*pi*t/50+.6*pi)))
plot.ts(cs_l+cs+5*w, main=expression(2*cos(2*pi*t/200+.6*pi)+2*cos(2*pi*t/50+.6*pi) + N(0,25)))
plot.ts(cs_l+cs, main=expression(2*cos(2*pi*t/200+.6*pi)+2*cos(2*pi*t/50+.6*pi)))

Tópicos em Séries Temporais

• Tendências;
  
• Filtragens;
  
• ARIMA, SARIMA, VARIMA;
  
• Cointegração;
  
• Estudo da volatilidade;
  
• Análise espectral;
  
• Modelos não-paramétricos;
  
• etc.

Bibliografia Complementar

• Morettin, P.A. e Toloi, C.M.C. (2004) Análise de Séries Temporais. Edgard Blücher.
  
• Brockwell, P.J., and Davis, R.A. (2002), Introduction Time Series and Forecasting, 2 ed. New York: Springer.
  
• Box, G.E.P., G.M. Jenkins and G.C. Reinsel (1994). Time Series Analysis, Forecasting, and Control, 3rd ed. Englewood Cliffs, NJ: Prentice Hall.
  
• Brillinger, D.R. (1975). Time Series: Data Analysis and Theory. New York: Holt, Rinehart & Winston Inc.
  
• Brockwell, P.J., and Davis, R.A. (1987), Time Series - Theory and Models. New York: Springer.
  
• Bloomfield, P. (2000). Fourier Analysis of Time Series: An Introduction, 2nd ed. New York: Wiley.
  
• Priestley, M.B. (1981). Spectral Analysis and Time Series. Vol. 1: Univariate Series; Vol 2: Multivariate Series, Prediction and Control. New York: Academic Press.
  
• Percival, D.B. and Waden A.T. (1999), Spectral Analysis for Physical Applications.
  
• Tsay, Ruey S. (2002). Analysis of Financial Time Series. New York: Wiley.
  
• Zivot, E. and Wang, J. (2006). Modeling Financial Time Series with S-PLUS. New York: Springer.