Seasonal Plots
Eric A. Suess
2/1/2021
Today we are going to take a look at a number of the time series datasets, tibbles, that are used in the fpp3 book that show seasonal patterns.
A seasonal pattern is one that is exhibited over and over again at regular intervals.
library(fpp3)## ── Attaching packages ────────────────────────────────────────────── fpp3 0.3 ──## ✓ tibble 3.0.5 ✓ tsibble 0.9.3
## ✓ dplyr 1.0.3 ✓ tsibbledata 0.2.0
## ✓ tidyr 1.1.2 ✓ feasts 0.1.6
## ✓ lubridate 1.7.9.2 ✓ fable 0.2.1
## ✓ ggplot2 3.3.3## ── Conflicts ───────────────────────────────────────────────── fpp3_conflicts ──
## x lubridate::date() masks base::date()
## x dplyr::filter() masks stats::filter()
## x tsibble::interval() masks lubridate::interval()
## x dplyr::lag() masks stats::lag()The book the author used the following code to create the a10 tsibble.
Most poeple consider the code here to be “sort of bad” code. Why?
Answer: The assignment to a new object in R is usually done at the start of a pipeline of code not at the end. It is easy to missing the assignment at the end.
PBS %>%
filter(ATC2 == "A10") %>%
select(Month, Concession, Type, Cost) %>%
summarise(TotalC = sum(Cost)) %>%
mutate(Cost = TotalC / 1e6) -> a10Beware of the is in the book. It may be hard to find code your are looking for because of this. Better practice.
a10 <- PBS %>%
filter(ATC2 == "A10") %>%
select(Month, Concession, Type, Cost) %>%
summarise(TotalC = sum(Cost)) %>%
mutate(Cost = TotalC / 1e6) # 1e6 = 1000000
a10## # A tsibble: 204 x 3 [1M]
## Month TotalC Cost
## <mth> <dbl> <dbl>
## 1 1991 Jul 3526591 3.53
## 2 1991 Aug 3180891 3.18
## 3 1991 Sep 3252221 3.25
## 4 1991 Oct 3611003 3.61
## 5 1991 Nov 3565869 3.57
## 6 1991 Dec 4306371 4.31
## 7 1992 Jan 5088335 5.09
## 8 1992 Feb 2814520 2.81
## 9 1992 Mar 2985811 2.99
## 10 1992 Apr 3204780 3.20
## # … with 194 more rowsa10 %>% autoplot()## Plot variable not specified, automatically selected `.vars = TotalC`
a10 %>% gg_season() # plots first column## Plot variable not specified, automatically selected `y = TotalC`## Warning in NextMethod("["): Incompatible methods (">=.Date", ">=.vctrs_vctr")
## for ">="## Warning in NextMethod("["): Incompatible methods ("<=.Date", "<=.vctrs_vctr")
## for "<="## Warning in NextMethod("["): Incompatible methods (">=.Date", ">=.vctrs_vctr")
## for ">="## Warning in NextMethod("["): Incompatible methods ("<=.Date", "<=.vctrs_vctr")
## for "<="
a10 %>%
gg_season(Cost, labels = "both") +
labs(y = "$ million",
title = "Seasonal plot: antidiabetic drug sales")## Warning in NextMethod("["): Incompatible methods (">=.Date", ">=.vctrs_vctr")
## for ">="## Warning in NextMethod("["): Incompatible methods ("<=.Date", "<=.vctrs_vctr")
## for "<="## Warning in NextMethod("["): Incompatible methods (">=.Date", ">=.vctrs_vctr")
## for ">="## Warning in NextMethod("["): Incompatible methods ("<=.Date", "<=.vctrs_vctr")
## for "<="
a10 %>% gg_subseries() # plots first column## Plot variable not specified, automatically selected `y = TotalC`
a10 %>%
gg_subseries(Cost) +
labs(y = "$ million",
title = "Seasonal subseries plot: antidiabetic drug sales")
Notice that there is an upward trend in the data. So the year is an important predictor of the TotalC.
Also notice the effect of the tend on the ACF.
a10 %>% gg_tsdisplay(TotalC)## Warning in NextMethod("["): Incompatible methods (">=.Date", ">=.vctrs_vctr")
## for ">="## Warning in NextMethod("["): Incompatible methods ("<=.Date", "<=.vctrs_vctr")
## for "<="## Warning in NextMethod("["): Incompatible methods (">=.Date", ">=.vctrs_vctr")
## for ">="## Warning in NextMethod("["): Incompatible methods ("<=.Date", "<=.vctrs_vctr")
## for "<="
Tourism
Filter the data to only look at trips where the purpose was a Holiday.
holidays <- tourism %>%
filter(Purpose == "Holiday") %>%
group_by(State) %>%
summarise(Trips = sum(Trips))
holidays## # A tsibble: 640 x 3 [1Q]
## # Key: State [8]
## State Quarter Trips
## <chr> <qtr> <dbl>
## 1 ACT 1998 Q1 196.
## 2 ACT 1998 Q2 127.
## 3 ACT 1998 Q3 111.
## 4 ACT 1998 Q4 170.
## 5 ACT 1999 Q1 108.
## 6 ACT 1999 Q2 125.
## 7 ACT 1999 Q3 178.
## 8 ACT 1999 Q4 218.
## 9 ACT 2000 Q1 158.
## 10 ACT 2000 Q2 155.
## # … with 630 more rowsholidays %>% autoplot(Trips) +
labs(y = "thousands of trips",
title = "Australian domestic holiday nights")
Compare two of the time series.
Victory is very well behaved Quarterly data.
holidays %>% filter(State == "Victoria") %>%
gg_tsdisplay()## Plot variable not specified, automatically selected `y = Trips`## Warning in NextMethod("["): Incompatible methods (">=.Date", ">=.vctrs_vctr")
## for ">="## Warning in NextMethod("["): Incompatible methods ("<=.Date", "<=.vctrs_vctr")
## for "<="## Warning in NextMethod("["): Incompatible methods (">=.Date", ">=.vctrs_vctr")
## for ">="## Warning in NextMethod("["): Incompatible methods ("<=.Date", "<=.vctrs_vctr")
## for "<="
ACT is not so well behaved.
holidays %>% filter(State == "ACT") %>%
gg_tsdisplay()## Plot variable not specified, automatically selected `y = Trips`## Warning in NextMethod("["): Incompatible methods (">=.Date", ">=.vctrs_vctr")
## for ">="## Warning in NextMethod("["): Incompatible methods ("<=.Date", "<=.vctrs_vctr")
## for "<="## Warning in NextMethod("["): Incompatible methods (">=.Date", ">=.vctrs_vctr")
## for ">="## Warning in NextMethod("["): Incompatible methods ("<=.Date", "<=.vctrs_vctr")
## for "<="
Scatterplots
Now, summing over all of the different Purposes within the States.
visitors <- tourism %>%
group_by(State) %>%
summarise(Trips = sum(Trips))
visitors ## # A tsibble: 640 x 3 [1Q]
## # Key: State [8]
## State Quarter Trips
## <chr> <qtr> <dbl>
## 1 ACT 1998 Q1 551.
## 2 ACT 1998 Q2 416.
## 3 ACT 1998 Q3 436.
## 4 ACT 1998 Q4 450.
## 5 ACT 1999 Q1 379.
## 6 ACT 1999 Q2 558.
## 7 ACT 1999 Q3 449.
## 8 ACT 1999 Q4 595.
## 9 ACT 2000 Q1 600.
## 10 ACT 2000 Q2 557.
## # … with 630 more rowsConsider the cross-correlation between the different time series from different States.
visitors %>%
ggplot(aes(x = Quarter, y = Trips)) +
geom_line() +
facet_grid(vars(State), scales = "free_y") +
labs(y = "Number of visitor nights each quarter (millions)")
The ggpairs() function assumes the different time series are down separate columns. Note that is changes a tidy tsibble into a non-tidy tsibble.
visitors %>%
pivot_wider(values_from=Trips, names_from=State) %>%
GGally::ggpairs(columns = 2:9)## Registered S3 method overwritten by 'GGally':
## method from
## +.gg ggplot2
Now consider the autocorrelation with since time series.
Can you see the autocorrelation every 4 Quarters in the Victoria time series?
visitors %>%
pivot_wider(values_from=Trips, names_from=State) %>%
select("Victoria") %>%
gg_lag(geom = "point")## Plot variable not specified, automatically selected `y = Victoria`
visitors %>%
pivot_wider(values_from=Trips, names_from=State) %>%
select("Victoria") %>%
ACF() %>%
autoplot()## Response variable not specified, automatically selected `var = Victoria`
Can you see that there is not so clear of a seasonal pattern in the ACT time series.
visitors %>%
pivot_wider(values_from=Trips, names_from=State) %>%
select("ACT") %>%
gg_lag(geom = "point")## Plot variable not specified, automatically selected `y = ACT`
visitors %>%
pivot_wider(values_from=Trips, names_from=State) %>%
select("ACT") %>%
ACF() %>%
autoplot()## Response variable not specified, automatically selected `var = ACT`