R中auto.arima模型选择的解释和再现

Question

在 RStudio 中，我在内置航空乘客数据 (AirPassengers) 上运行 auto.arima。数据似乎呈倍增趋势。预测结果似乎相当准确。

# Load the corresponging library.
library(forecast)

# Save the default parameters.
defaultPar <- par(no.readonly = TRUE)

# Prepare a graph of four (2x2) subgraphs
par(mfrow = c(3, 1))

# Fit the model. Use the built in AirPassengers data.
modelAA <- auto.arima(AirPassengers)

plot(AirPassengers, 
     main = 'Air passengers', 
     col = 'purple',
     ylab = 'Passengers number', 
     xlab = 'Year')

plot(forecast(modelAA, 24), 
     main = 'Air passengers + auto.arima forecasting', 
     col = 'red',
     ylab = 'Passengers number', 
     xlab = 'Year')

qqnorm(modelAA$residuals, col = 'red')
qqline(modelAA$residuals, col = 'green')

# Restore the default parameters.
par(defaultPar)

如以下代码示例所示，自动 ARIMA 预测已选择以下模型：(2, 1, 1)(0, 1, 0)[12]。

print(modelAA)
Series: AirPassengers 
ARIMA(2,1,1)(0,1,0)[12] 

Coefficients:
         ar1     ar2      ma1
      0.5960  0.2143  -0.9819
s.e.  0.0888  0.0880   0.0292

sigma^2 estimated as 132.3:  log likelihood=-504.92
AIC=1017.85   AICc=1018.17   BIC=1029.35

如何解释自动选择 (2, 1, 1)(0, 1, 0)[12] 并通过调用 arima(x, order = c()...) 重现它？谢谢。

Answer 1

这是一个季节性有马模型。您可以从enter link description here获取详细信息。

当你调用arimafunction (x, order = c(0L, 0L, 0L), seasonal = list(order = c(0L, 0L, 0L), period = NA), xreg = NULL, include.mean = TRUE, transform.pars = TRUE, fixed = NULL, init = NULL, method = c("CSS-ML", "ML", "CSS"), n.cond, SSinit = c("Gardner1980", "Rossignol2011"), optim.method = "BFGS", optim.control = list(), kappa = 1e+06) 时，你应该设置paras order/sensonal/period where period = 12。