使用 ARIMA 模型估算缺失值 [英] Imputing missing values using ARIMA model

问题描述

我正在尝试使用 R 中的 ARIMA 模型来估算时间序列中的缺失值.我尝试了这段代码，但没有成功.

I am trying to impute missing values in a time series with an ARIMA model in R. I tried this code but no success.

x <- AirPassengers
x[90:100] <- NA
fit <- auto.arima(x)
fitted(fit)[90:100]  ## this is giving me NAs
plot(x)
lines(fitted(fit), col="red")

拟合模型没有估算缺失值.关于这是如何完成的任何想法?

The fitted model is not imputing the missing values. Any idea on how this is done?

推荐答案

fitted 提供样本内的一步预测.做你想做的事情的正确"方法是通过卡尔曼平滑器.使用缺失部分的前向和后向预测的平均值可以获得对大多数目的来说足够好的粗略近似值.像这样:

fitted gives in-sample one-step forecasts. The "right" way to do what you want is via a Kalman smoother. A rough approximation good enough for most purposes is obtained using the average of the forward and backward forecasts for the missing section. Like this:

x <- AirPassengers
x[90:100] <- NA
fit <- auto.arima(x)
fit1 <- forecast(Arima(AirPassengers[1:89],model=fit),h=10)
fit2 <- forecast(Arima(rev(AirPassengers[101:144]), model=fit), h=10)

plot(x)
lines(ts(0.5*c(fit1$mean+rev(fit2$mean)), 
  start=time(AirPassengers)[90],freq=12), col="red")

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