Time Series

Example) nottem

Description : Monthly temperature data (Nottingham, UK)

library(prophet)

## Warning: package 'prophet' was built under R version 4.4.3

## Loading required package: Rcpp

## Warning: package 'Rcpp' was built under R version 4.4.3

## Loading required package: rlang

data(nottem)
nottem

##       Jan  Feb  Mar  Apr  May  Jun  Jul  Aug  Sep  Oct  Nov  Dec
## 1920 40.6 40.8 44.4 46.7 54.1 58.5 57.7 56.4 54.3 50.5 42.9 39.8
## 1921 44.2 39.8 45.1 47.0 54.1 58.7 66.3 59.9 57.0 54.2 39.7 42.8
## 1922 37.5 38.7 39.5 42.1 55.7 57.8 56.8 54.3 54.3 47.1 41.8 41.7
## 1923 41.8 40.1 42.9 45.8 49.2 52.7 64.2 59.6 54.4 49.2 36.3 37.6
## 1924 39.3 37.5 38.3 45.5 53.2 57.7 60.8 58.2 56.4 49.8 44.4 43.6
## 1925 40.0 40.5 40.8 45.1 53.8 59.4 63.5 61.0 53.0 50.0 38.1 36.3
## 1926 39.2 43.4 43.4 48.9 50.6 56.8 62.5 62.0 57.5 46.7 41.6 39.8
## 1927 39.4 38.5 45.3 47.1 51.7 55.0 60.4 60.5 54.7 50.3 42.3 35.2
## 1928 40.8 41.1 42.8 47.3 50.9 56.4 62.2 60.5 55.4 50.2 43.0 37.3
## 1929 34.8 31.3 41.0 43.9 53.1 56.9 62.5 60.3 59.8 49.2 42.9 41.9
## 1930 41.6 37.1 41.2 46.9 51.2 60.4 60.1 61.6 57.0 50.9 43.0 38.8
## 1931 37.1 38.4 38.4 46.5 53.5 58.4 60.6 58.2 53.8 46.6 45.5 40.6
## 1932 42.4 38.4 40.3 44.6 50.9 57.0 62.1 63.5 56.3 47.3 43.6 41.8
## 1933 36.2 39.3 44.5 48.7 54.2 60.8 65.5 64.9 60.1 50.2 42.1 35.8
## 1934 39.4 38.2 40.4 46.9 53.4 59.6 66.5 60.4 59.2 51.2 42.8 45.8
## 1935 40.0 42.6 43.5 47.1 50.0 60.5 64.6 64.0 56.8 48.6 44.2 36.4
## 1936 37.3 35.0 44.0 43.9 52.7 58.6 60.0 61.1 58.1 49.6 41.6 41.3
## 1937 40.8 41.0 38.4 47.4 54.1 58.6 61.4 61.8 56.3 50.9 41.4 37.1
## 1938 42.1 41.2 47.3 46.6 52.4 59.0 59.6 60.4 57.0 50.7 47.8 39.2
## 1939 39.4 40.9 42.4 47.8 52.4 58.0 60.7 61.8 58.2 46.7 46.6 37.8

df <- data.frame(
  ds = seq.Date(
    from = as.Date("1920-01-01"),
    by   = "month",
    length.out = length(nottem)
  ),
  temp = as.numeric(nottem)
)

Brief Visualzation – linear mdl

plot(df$ds, df$temp, type = "l",
     main = "Monthly Temperatures (Nottingham)",
     xlab = "Year", ylab = "Temperature")

linear_mdl <- lm(temp~ds, data=df)
abline(linear_mdl, col="red")

• As we can see, describing this linearly is silly – there are clear non-linear trends

Monthly seasonal trends :

library(prophet)

# rename column
df_prophet <- df
names(df_prophet)[2] <- "y"

# 1. initialize model (NO data here)
m <- prophet(
  weekly.seasonality = FALSE,
  daily.seasonality  = FALSE,
  yearly.seasonality = FALSE
)

# 2. add monthly seasonality BEFORE fitting
m <- add_seasonality(
  m,
  name = "monthly",
  period = 30.5,
  fourier.order = 5
) 


# 3. now fit
m <- fit.prophet(m, df_prophet)

future <- make_future_dataframe(m, periods = 24, freq = "month")
forecast <- predict(m, future)

plot(m, forecast)