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.
── Attaching packages ──────────────────────────────────────────── fpp3 0.4.0 ──
✔ tibble 3.1.7 ✔ tsibble 1.1.1
✔ dplyr 1.0.9 ✔ tsibbledata 0.4.0
✔ tidyr 1.2.0 ✔ feasts 0.2.2
✔ lubridate 1.8.0 ✔ fable 0.3.1
✔ ggplot2 3.3.6
── Conflicts ───────────────────────────────────────────────── fpp3_conflicts ──
✖ lubridate::date() masks base::date()
✖ dplyr::filter() masks stats::filter()
✖ tsibble::intersect() masks base::intersect()
✖ tsibble::interval() masks lubridate::interval()
✖ dplyr::lag() masks stats::lag()
✖ tsibble::setdiff() masks base::setdiff()
✖ tsibble::union() masks base::union()
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.
%>% filter (ATC2 == "A10" ) %>% select (Month, Concession, Type, Cost) %>% summarise (TotalC = sum (Cost)) %>% mutate (Cost = TotalC / 1e6 ) -> a10
Beware of the is in the book. It may be hard to find code your are looking for because of this. Better practice.
<- PBS %>% filter (ATC2 == "A10" ) %>% select (Month, Concession, Type, Cost) %>% summarise (TotalC = sum (Cost)) %>% mutate (Cost = TotalC / 1e6 ) # 1e6 = 1000000
# 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 rows
Plot variable not specified, automatically selected `.vars = TotalC`
write.csv (a10, "a10.csv" )
%>% gg_season () # plots first column
Plot variable not specified, automatically selected `y = TotalC`
%>% gg_season (Cost, labels = "both" ) + labs (y = "$ million" ,title = "Seasonal plot: antidiabetic drug sales" )
%>% gg_subseries () # plots first column
Plot variable not specified, automatically selected `y = TotalC`
%>% 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.
%>% gg_tsdisplay (TotalC)
Tourism
Filter the data to only look at trips where the purpose was a Holiday.
<- tourism %>% filter (Purpose == "Holiday" ) %>% group_by (State) %>% summarise (Trips = sum (Trips))
# 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 rows
%>% 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.
%>% filter (State == "Victoria" ) %>% gg_tsdisplay ()
Plot variable not specified, automatically selected `y = Trips`
%>% filter (State == "Victoria" ) %>% write.csv ("victoria.csv" )%>% filter (State == "Victoria" ) %>% ACF ()
Response variable not specified, automatically selected `var = Trips`
# A tsibble: 19 x 3 [1Q]
# Key: State [1]
State lag acf
<chr> <lag> <dbl>
1 Victoria 1Q 0.00755
2 Victoria 2Q -0.452
3 Victoria 3Q 0.0374
4 Victoria 4Q 0.828
5 Victoria 5Q -0.0305
6 Victoria 6Q -0.463
7 Victoria 7Q 0.0289
8 Victoria 8Q 0.730
9 Victoria 9Q -0.0735
10 Victoria 10Q -0.442
11 Victoria 11Q -0.00197
12 Victoria 12Q 0.660
13 Victoria 13Q -0.0687
14 Victoria 14Q -0.422
15 Victoria 15Q -0.0160
16 Victoria 16Q 0.594
17 Victoria 17Q -0.0975
18 Victoria 18Q -0.426
19 Victoria 19Q -0.0346
%>% filter (State == "Victoria" ) %>% ACF () %>% autoplot ()
Response variable not specified, automatically selected `var = Trips`
ACT is not so well behaved.
%>% filter (State == "ACT" ) %>% gg_tsdisplay ()
Plot variable not specified, automatically selected `y = Trips`
Scatterplots
Now, summing over all of the different Purposes within the States.
<- tourism %>% group_by (State) %>% summarise (Trips = sum (Trips))
# 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 rows
Consider the cross-correlation between the different time series from different States.
%>% 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.
%>% pivot_wider (values_from= Trips, names_from= State) %>% :: 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?
%>% pivot_wider (values_from= Trips, names_from= State) %>% select ("Victoria" ) %>% gg_lag (geom = "point" )
Plot variable not specified, automatically selected `y = Victoria`
%>% 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.
%>% pivot_wider (values_from= Trips, names_from= State) %>% select ("ACT" ) %>% gg_lag (geom = "point" )
Plot variable not specified, automatically selected `y = ACT`
%>% pivot_wider (values_from= Trips, names_from= State) %>% select ("ACT" ) %>% ACF () %>% autoplot ()
Response variable not specified, automatically selected `var = ACT`
