Groupby one column and calculate lag difference of monthly, quarterly mixed data's current period values with previous one using R

Question

Assuming I have a panel data as follows, which was edited from this link:

df <- structure(list(id = structure(c(1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 
2L, 2L, 2L, 2L, 2L, 2L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 3L), .Label = c("M01", 
"M02", "S01"), class = "factor"), date = structure(c(2L, 3L, 
4L, 5L, 6L, 7L, 8L, 2L, 3L, 4L, 5L, 6L, 7L, 8L, 1L, 2L, 3L, 4L, 
5L, 6L, 7L, 8L), .Label = c("2020-12", "2021-01", "2021-02", 
"2021-03", "2021-04", "2021-05", "2021-06", "2021-07"), class = "factor"), 
    actual = c(3.4, 5.4, 7.4, 7.4, 7.5, 8, 8.9, 10.8, 10.1, 8.2, 
    10.1, 9.4, 10.1, 9.4, -0.3, NA, NA, 8.6, NA, NA, 8.3, NA), 
    pred = c(3.288889774, 5.819407687, 6.705608369, 6.054457292, 
    5.582409131, 7.01052472, 9.742902434, 10.98571396, 6.522003651, 
    9.688977242, 10.39801463, 9.398991615, 9.764616936, 9.855033457, 
    0.493311422, 8.403722942, 8.174854517, 8.573117852, 8.403065801, 
    8.684289455, 8.719079247, 8.259439468)), class = "data.frame", row.names = c(NA, 
-22L)) 

After groupby id, for each month's actual and predicted values, I need to calculate current month's actual and predicted values with previous month's actual values, except: let's say for id=='S01', it's a quarterly data instead of monthly, so I'll need calculate difference values by current month's with previous quarter's last month's actual values, ie., in 2021-03's with 2020-12's instead of 2021-02, same logic for other months.

My attempt code:

df %>% 
  group_by(id) %>% 
  mutate(actual2=actual) %>% 
  fill(actual2) %>% 
  mutate(act_diff = case_when(
    actual2 > lag(actual2) ~ actual2 - lag(actual2), 
    actual2 < lag(actual2) ~ actual2 - lag(actual2), 
    actual2 == lag(actual2) ~ 0), 
    pred_diff = case_when(
      pred > lag(actual2) ~ pred - lag(actual2), 
      pred < lag(actual2) ~ pred - lag(actual2), 
      pred == lag(actual2) ~ 0), 
    act_diff = ifelse((id=='S01')&is.na(actual), NA, act_diff),
    pred_diff = ifelse((id=='S01')&is.na(actual), NA, pred_diff), actual2=NULL) %>%
  print(n=22)

Result:

   id    date    actual   pred act_diff pred_diff
   <fct> <fct>    <dbl>  <dbl>    <dbl>     <dbl>
 1 M01   2021-01    3.4  3.29    NA        NA    
 2 M01   2021-02    5.4  5.82     2         2.42 
 3 M01   2021-03    7.4  6.71     2         1.31 
 4 M01   2021-04    7.4  6.05     0        -1.35 
 5 M01   2021-05    7.5  5.58     0.100    -1.82 
 6 M01   2021-06    8    7.01     0.5      -0.489
 7 M01   2021-07    8.9  9.74     0.9       1.74 
 8 M02   2021-01   10.8 11.0     NA        NA    
 9 M02   2021-02   10.1  6.52    -0.700    -4.28 
10 M02   2021-03    8.2  9.69    -1.9      -0.411
11 M02   2021-04   10.1 10.4      1.9       2.20 
12 M02   2021-05    9.4  9.40    -0.700    -0.701
13 M02   2021-06   10.1  9.76     0.700     0.365
14 M02   2021-07    9.4  9.86    -0.700    -0.245
15 S01   2020-12   -0.3  0.493   NA        NA    
16 S01   2021-01   NA    8.40    NA        NA    
17 S01   2021-02   NA    8.17    NA        NA    
18 S01   2021-03    8.6  8.57     8.9       8.87 
19 S01   2021-04   NA    8.40    NA        NA    
20 S01   2021-05   NA    8.68    NA        NA    
21 S01   2021-06    8.3  8.72    -0.300     0.119
22 S01   2021-07   NA    8.26    NA        NA 

How could I modify the code above get an expected outcome like this? Thanks:

    id    date actual       pred act_diff  pred_diff
1  M01 2021-01    3.4  3.2888898       NA         NA
2  M01 2021-02    5.4  5.8194077      2.0  2.4194077
3  M01 2021-03    7.4  6.7056084      2.0  1.3056084
4  M01 2021-04    7.4  6.0544573      0.0 -1.3455427
5  M01 2021-05    7.5  5.5824091      0.1 -1.8175909
6  M01 2021-06    8.0  7.0105247      0.5 -0.4894753
7  M01 2021-07    8.9  9.7429024      0.9  1.7429024
8  M02 2021-01   10.8 10.9857140       NA         NA
9  M02 2021-02   10.1  6.5220037     -0.7 -4.2779963
10 M02 2021-03    8.2  9.6889772     -1.9 -0.4110228
11 M02 2021-04   10.1 10.3980146      1.9  2.1980146
12 M02 2021-05    9.4  9.3989916     -0.7 -0.7010084
13 M02 2021-06   10.1  9.7646169      0.7  0.3646169
14 M02 2021-07    9.4  9.8550335     -0.7 -0.2449665
15 S01 2020-12   -0.3  0.4933114       NA         NA
16 S01 2021-01     NA  8.4037229       NA  8.7037229  # calculate with S01's actual value in 2020-12
17 S01 2021-02     NA  8.1748545       NA  8.4748545  # calculate with S01's actual value in 2020-12
18 S01 2021-03    8.6  8.5731179      8.9  8.8731179  # calculate with S01's actual value in 2020-12
19 S01 2021-04     NA  8.4030658       NA -0.1969342  # calculate with S01's actual value in 2021-03
20 S01 2021-05     NA  8.6842895       NA  0.0842895  # calculate with S01's actual value in 2021-03
21 S01 2021-06    8.3  8.7190792     -0.3  0.1190792  # calculate with S01's actual value in 2021-03
22 S01 2021-07     NA  8.2594395       NA -0.0405605  # calculate with S01's actual value in 2021-06