Moving averages and Decomposition

Moving averages

Code

library(fpp3)
library(tidyverse)

# ggplot theme: 
theme_set(theme_bw() + 
            theme(panel.grid.major = element_blank(),
                  panel.grid.minor = element_blank()))

# -- Read in data: --
dat <- readxl::read_excel(
  "data/NorwayEmployment_15-74years_bySex.xlsx") %>%
  as_tibble() %>%
  mutate(Quarter = str_replace(Quarter, "K","Q"),
         Quarter = yearquarter(Quarter)) 
names(dat)[3] <- "Employed"

# -- Aggregating from Employed by sex to total --
dat <- dat %>% 
  group_by(Quarter) %>% 
  summarize(Employed = sum(Employed)) %>%
  as_tsibble(index = Quarter) # Time series table
dat %>% 
  autoplot(Employed, colour = "blue")

dat <- dat %>%
  mutate(
    `12-MA` = slider::slide_dbl(Employed, mean,
                                .before = 5, .after = 6, .complete = TRUE),
    `2x12-MA` = slider::slide_dbl(`12-MA`, mean,
                                  .before = 1, .after = 0, .complete = TRUE)
  )
dat %>%
  ggplot(aes(x=Quarter, y =Employed))+
  geom_line(colour = "gray") +
  geom_line(aes(y = `2x12-MA`), colour = "#D55E00") +
  theme_bw()+
  labs(y = "Persons (thousands)",
       title = "Total employment in US retail")

Warning: Removed 12 rows containing missing values (`geom_line()`).

Classical decomposition

Code

dat %>% 
  model(
    classical_decomposition(Employed, type = "additive")
  ) %>%
  components() %>%
  autoplot()

Warning: Removed 2 rows containing missing values (`geom_line()`).

Statistics agencies: X11 and SEATS

Code

dat %>% 
  model(
    classical = classical_decomposition(Employed, 
                                        type = "multiplicative"),
    x11 = X_13ARIMA_SEATS(Employed ~ x11()),
    seats = X_13ARIMA_SEATS(Employed ~ seats())
  ) %>%
  components() %>% 
  mutate(random = ifelse(.model == "classical", 
                         random, 
                         irregular)) %>%
  autoplot()

Warning: Removed 2 rows containing missing values (`geom_line()`).

STL: Seasonal and Trend decomposition using Loess

Code

dat %>%
  model(
    STL0 = STL(Employed),
    STL1 = STL(Employed ~ trend(window = 5) + # default 7
                 season(window = 19),         # default 11
               robust = FALSE)
  ) %>%
  components() %>%
  autoplot()