You need to reshape your data into a long format, also for future posts please share your data on a copy/paste friendly format, like in this example:
dataset6 <- data.frame(
Year = c(1953L, 1954L, 1955L, 1956L, 1957L, 1958L, 1959L, 1960L, 1961L),
Jan = c(26.8, 27.1, 26.9, 26.8, 26.3, 27.1, 27.1, 26.3, 27),
Feb = c(27.2, 27.5, 26.3, 26.9, 27.1, 27.1, 27.5, 26.7, 27.4),
Mar = c(27.1, 27.4, 25.7, 26.7, 26.2, 27.4, 26.2, 26.6, 27),
Apr = c(26.3, 26.4, 25.7, 26.1, 25.7, 26.4, 28.2, 25.8, 26.3),
May = c(25.4, 24.8, 24.8, 26.2, 25.5, 25.5, 27.1, 25.2, 25.9),
Jun = c(23.9, 24.3, 24, 24.7, 24.9, 24.7, 25.4, 25.1, 24.6),
Jul = c(23.8, 23.4, 23.4, 23.9, 24.2, 24.3, 25.6, 23.3, 24.1),
Aug = c(23.6, 23.4, 23.5, 23.7, 24.6, 24.4, 24.5, 23.8, 24.3),
Sep = c(25.3, 24.6, 24.8, 24.7, 25.5, 24.8, 24.7, 25.2, 25.2),
Oct = c(25.8, 25.4, 25.6, 25.8, 25.9, 26.2, 26, 25.5, 26.3),
Nov = c(26.4, 25.8, 26.2, 26.1, 26.4, 26.3, 26.5, 26.4, 26.4),
Dec = c(26.9, 26.7, 26.5, 26.5, 26.9, 27, 26.8, 26.7, 26.7)
)
library(tidyverse)
library(lubridate)
dataset6 %>%
gather(Month, Value, -Year) %>%
transmute(Month = ymd(paste(Year, Month, "01", sep = "-")),
Value = Value) %>%
arrange(Month) %>%
select(-Month) %>%
ts(start = c(1953, 1), end = c(1961, 12),
frequency = 12) %>%
plot()
