ARIMA - integrated ARMA

ARIMA Models in R

David Stoffer

Professor of Statistics at the University of Pittsburgh

Identifying ARIMA

A time series exhibits ARIMA behavior if the differenced data has ARMA behavior

# Simulation  ARIMA(p = 1, d = 1, q = 0)
x <- arima.sim(list(order = c(1, 1, 0),  ar = .9), n = 200)
plot(x, main = "ARIMA(p = 1, d = 1, q = 0)")
plot(diff(x), main = "ARMA(p = 1, d = 0, q = 0)")

ch3_1.012.png

ACF and PCF of an Integrated ARMA

x <- arima.sim(list(order = c(1, 1, 0),  ar = .9), n = 200)
acf2(x)

ch3_1.015.png

ACF and PCF of a Differenced ARIMA

x <- arima.sim(list(order = c(1, 1, 0),  ar = .9), n = 200)
acf2(diff(x))

ch3_1.018.png

ACF and PCF of a Differenced ARIMA

x <- arima.sim(list(order = c(1, 1, 0),  ar = .9), n = 200)
acf2(diff(x))

ch3_1.019.png

Weekly Oil Prices

ch3_1.021.png

Weekly Oil Prices

ch3_1.022.png

Looks like ARIMA(1, 1, 1)

Let's practice!

ARIMA Models in R