Indexing a set of time series to compare % changes from baseline

References:

1. Don’t use dual-scaled y-axes : https://www.perceptualedge.com/articles/visual_business_intelligence/dual-scaled_axes.pdf
2. Simple guide to indexing : https://www.dallasfed.org/research/basics/indexing.aspx

Original data

df1.data <- 
    tibble::tribble(
        ~time, ~x1, ~x2,
            1,  25, 432,
            2,  28, 440,
            3,  32, 590,
            4,  20, 328,
            5,  40, 500,
            6,  44, 600,
            7,  42, 605,
            8,  50, 650,
            9,  55, 700,
           10,  60, 710
        )


df1.data %>% 
    kable() %>% 
    kable_styling(bootstrap_options = c("striped", 
                                        "responsive"), 
                  full_width = F, 
                  position = "left")

Plot without indexing

df1.data %>% 
    gather(key = metric, 
           value = value, 
           -time) %>% 
    ggplot(aes(x = time, 
               y = value, 
               group = metric, 
               col = metric)) + 
    geom_line() + 
    labs(title = "Not very easy to compare growth rates", 
         subtitle = "Metrics have different scales which are not directly comparable")

Define function to index a column

# function for indexing: 
index_function <- function(x){
    # input: x, a vector
    # output: x_indexed, a vector 
    
    initial <- x[1]
    
    x_indexed <- map_dbl(x, function(x){x/initial * 100})
    
    return(x_indexed)
    
}


# test the function: 
# x <- c(12, 24, 120, 1200)
# index_function(x)

Index the columns X1 and X2

# now index the 2 series: 
df2.indexed <- 
    df1.data %>% 
    mutate(x1_indexed = index_function(x1), 
           x2_indexed = index_function(x2))


df2.indexed %>% 
    kable() %>% 
    kable_styling(bootstrap_options = c("striped", 
                                        "responsive"), 
                  full_width = F, 
                  position = "left")

Plot after indexing

df2.indexed %>% 
    select(time, 
           x1_indexed, 
           x2_indexed) %>% 
    gather(key = metric, 
           value = value, 
           -time) %>% 
    ggplot(aes(x = time, 
               y = value, 
               group = metric, 
               col = metric)) + 
    geom_line() + 
    geom_hline(yintercept = 100, 
               col = "blue") + 
    labs(title = "Indexing the series makes growth rates easy to compare", 
         subtitle = "Each metric starts at 100, subsequent points show value as a % of initial value")