ARIMA——差分整合的ARMA

R 中的 ARIMA 模型

David Stoffer

Professor of Statistics at the University of Pittsburgh

识别 ARIMA

若差分后的数据呈现 ARMA 行为，则该时间序列呈现 ARIMA 行为

# 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

积分 ARMA 的 ACF 与 PACF

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

ch3_1.015.png

差分后 ARIMA 的 ACF 与 PACF

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

ch3_1.018.png

差分后 ARIMA 的 ACF 与 PACF

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

ch3_1.019.png

每周原油价格

ch3_1.021.png

每周原油价格

ch3_1.022.png

看起来是 ARIMA(1, 1, 1)

Passons à la pratique !

R 中的 ARIMA 模型