R中的滞后回归:确定最佳滞后 [英] Lagged regression in R: determining the optimal lag

问题描述

我有一个变量，被认为可以很好地预测另一个变量，但是有些滞后.我不知道滞后是什么，想从数据中估算出来.

I have a variable that is believed to be a good predictor for another variable, but with some lag. I don't know what the lag is and want to estimate it from the data.

这是一个例子:

library(tidyverse)

data <- tibble(
  id = 1:100,
  y = dnorm(1:100, 30, 20) * 1000,
  x.shifted = y / 10 + runif(100) / 10,
  x.actual = lag(x.shifted, 30)
)

data %>% 
  ggplot(aes(id, x.shifted)) +
  geom_point() +
  geom_point(aes(id, x.actual), color = 'blue') +
  geom_point(aes(id, y), color = 'red')

模型 lm(y〜x.actual，data)不太合适，但是模型 lm(y〜x.shifted，data)是.在这里，我知道x必须偏移-30天，但想象一下我没有，我只知道它在-30到+30之间.

The model lm(y ~ x.actual, data) would not be a great fit, but the model lm(y ~ x.shifted, data) would be. Here, I know that x must be shifted by -30 days, but imagine I did not and all I knew was that it is between -30 and +30.

我想到的直接方法是运行61个回归模型，从将x偏移-30的模型到将x偏移+30的模型，然后选择具有最佳AIC或BIC的模型.但是(a)这是正确的方法吗?(b)是否已经有R包已经这样做并找到了最佳滞后?

The immediate approach that comes to mind is to run 61 regression models, from one that shifts x by -30 to the one that shifts it by +30, and then pick the model with the best AIC or BIC. However, (a) is this the correct approach, and (b) are there R packages that already do this and find the optimal lag?

推荐答案

您所描述的是两个变量的互相关.您可以在 R 中使用 ccf 轻松完成此操作.

What you are describing is the cross-correlation of the two variables. You can do this very easily in R with ccf.

但是，为了获得最佳的滞后，我们可以使用 sapply 将所需的滞后次数输入到 cor 函数中，从而简化为单行代码使用 which.max 来找到最高的相关性:

However, to just get the optimum lags, we can simplify to a one-liner by using sapply to feed the number of required lags into the cor function, then use which.max to find the highest correlation:

which.max(sapply(1:50, function(i) cor(data$x.actual, lag(data$y, i), use = "complete")))
#> [1] 30

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