Replacing missing values

Question

Let's say I have a dataframe containing the sales for some quarters, while the values for the following quarters are missing. I would like to replace the NAs by a simple formula (with mutate/dplyr like below). The issue is that I don't want to use mutate so many times. How could I do that for all NAs at the same time? Is there a way?

structure(list(Period = c("1999Q1", "1999Q2", "1999Q3", "1999Q4", 
"2000Q1", "2000Q2", "2000Q3", "2000Q4", "2001Q1", "2001Q2", "2001Q3", 
"2001Q4", "2002Q1", "2002Q2", "2002Q3", "2002Q4", "2003Q1", "2003Q2", 
"2003Q3", "2003Q4"), Sales= c(353.2925571, 425.9299841, 357.5204626, 
363.80247, 302.8081066, 394.328576, 435.15573, 387.99768, NA, 
NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA)), class = "data.frame", row.names = c(NA, 
-20L))

test %>%
      mutate(Sales = ifelse(is.na(Sales), 1.05*lag(Sales, 4), Sales)) %>%
      mutate(Sales = ifelse(is.na(Sales), 1.05*lag(Sales, 4), Sales)) %>%
      mutate(Sales = ifelse(is.na(Sales), 1.05*lag(Sales, 4), Sales))

Answer 1

One dplyr and tidyr possibility could be:

df %>%
 group_by(quarter = substr(Period, 5, 6)) %>%
 mutate(Sales_temp = replace_na(Sales, last(na.omit(Sales)))) %>%
 group_by(quarter, na = is.na(Sales)) %>%
 mutate(constant = 1.05,
        Sales_temp = Sales_temp * cumprod(constant),
        Sales = coalesce(Sales, Sales_temp)) %>%
 ungroup() %>%
 select(1:2)

   Period Sales
   <chr>  <dbl>
 1 1999Q1  353.
 2 1999Q2  426.
 3 1999Q3  358.
 4 1999Q4  364.
 5 2000Q1  303.
 6 2000Q2  394.
 7 2000Q3  435.
 8 2000Q4  388.
 9 2001Q1  318.
10 2001Q2  414.
11 2001Q3  457.
12 2001Q4  407.
13 2002Q1  334.
14 2002Q2  435.
15 2002Q3  480.
16 2002Q4  428.
17 2003Q1  351.
18 2003Q2  456.
19 2003Q3  504.
20 2003Q4  449.

Or with just dplyr:

df %>%
 group_by(quarter = substr(Period, 5, 6)) %>%
 mutate(Sales_temp = if_else(is.na(Sales), last(na.omit(Sales)), Sales)) %>%
 group_by(quarter, na = is.na(Sales)) %>%
 mutate(constant = 1.05,
        Sales_temp = Sales_temp * cumprod(constant),
        Sales = coalesce(Sales, Sales_temp)) %>%
 ungroup() %>%
 select(1:2)

Answer 2

x <- test$Sales

# find that last non-NA data
last.valid <- tail(which(!is.na(x)),1)

# store the "base"
base <- ceiling(last.valid/4)*4 + (-3:0)
base <- base + ifelse(base > last.valid, -4, 0)
base <- x[base]


# calculate the "exponents"
expos <- ceiling( ( seq(length(x)) - last.valid ) / 4 )

test$Sales <- ifelse(is.na(x), bases * 1.05 ^ expos, x)

tail(test)

#    Period    Sales
# 15 2002Q3 479.7592
# 16 2002Q4 427.7674
# 17 2003Q1 350.5382
# 18 2003Q2 456.4846
# 19 2003Q3 503.7472
# 20 2003Q4 449.1558