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在原始数据上绘制拟合的 ARIMA 结果时，拟合值有时会出现一个时间步长：

library(forecast)
set.seed(1)
#simualted ts
eg <- arima.sim(n = 100, list(order = c(1,1,2), ar =  -0.5, ma = c(.1, -0.3)),
                sd = 1)
#fitted Arima with same order
eg_aa <- forecast::Arima(eg, order = c(1,1,2))

par(mfrow = c(2,1),
    oma = c(0,0,0,0), 
    mar = c(2,4,1,1))
plot(eg,  main="as-is") # plot original sim
lines(fitted(eg_aa), col = "red") # plot fitted values
legend("topleft", legend = c("original","fitted"), col = c("black","red"),lty = 1)

plot(eg, main = "time-deltat") # plot original sim
points(time(fitted(eg_aa))-deltat(eg), # plot fitted values shifted back one time-step
       fitted(eg_aa),
       type = "l", col = "red")

剧情

但并非总是如此，拟合值在此示例中排列：in-r-plot-arima-fitted-model-with-the-original-series

根据我在时间序列课程中的记忆，曾经有差异的模型应该只适合第一次之后的观察，所以我不清楚 arima() 在哪里得到 t=1 拟合。但最重要的是，我想知道明显的时移是错误还是 arima 模型的奇怪结果。有任何想法吗？

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