groupwise avg基于上一时间段的userID

Question

我想创建一个新变量，它是partiucular userID的3个月平均值。

df <- data.frame(
  dates = seq(as.Date('2018-01-01'), as.Date('2018-12-01'), by = "month"),
  user_id = c("a","b","c","a","b","c","a","b","c","a","b","c"),
  somenum = 1:12
)

 df
        dates user_id somenum
1  2018-01-01       a       1
2  2018-02-01       b       2
3  2018-03-01       c       3
4  2018-04-01       a       4
5  2018-05-01       b       5
6  2018-06-01       c       6
7  2018-07-01       a       7
8  2018-08-01       b       8
9  2018-09-01       c       9
10 2018-10-01       a      10
11 2018-11-01       b      11
12 2018-12-01       c      12

示例，第10行（对应于用户“a”）的新变量的值为mean(10 + 7 + 4) = 7。

我怎么能这样做？理想情况下，在tidyverse / dplyr。