Exercises

Forecasting: Principles and Practice (3rd ed)
Chapter 2 Time series graphics

2.1

Explore the following four time series: Bricks from aus_production, Lynx from pelt, Close from gafa_stock, Demand from vic_elec.

  • Use ? (or help()) to find out about the data in each series.
# ?aus_production
# ?pelt
# ?gafa_stock
# ?vic_elec
  • What is the time interval of each series?
    • aus_production: quarterly
    • pelt: annual
    • gafa_stock: irregular days
    • vic_elec: half-hourly
  • Use autoplot()to produce a time plot of each series.
  • For the last plot, modify the axis labels and title.
aus_production |>
  autoplot(Bricks) +
  labs(y='Million Units', title='Australian Quarterly Bricks Prodcution') +
  theme_minimal()
## Warning: Removed 20 rows containing missing values or values outside the scale range
## (`geom_line()`).

pelt |>
  autoplot(Lynx) +
  labs(y='Pelts Traded', title='Hudson Bay Company Annual Lynx Pelts Traded') +
  theme_minimal()

gafa_stock |>
  autoplot(Close) +
  labs(y='$USD', title='GAFA Daily Closing Stock Prices') +
  theme_minimal()

vic_elec |>
  autoplot(Demand) +
  labs(y='MWh', title='Victoria, Australia Half-hourly Electricity Demand') +
  theme_minimal()

2.2

Use filter() to find what days corresponded to the peak closing price for each of the four stocks in gafa_stock.

max_close_dates = gafa_stock |>
  group_by(Symbol) |>
  filter(Close == max(Close)) |>
  ungroup() |>
  select(Date)

knit_table(max_close_dates, caption='Days corresponding to the peak closing price for each stock')
Days corresponding to the peak closing price for each stock
Date Symbol
2018-10-03 AAPL
2018-09-04 AMZN
2018-07-25 FB
2018-07-26 GOOG

2.3

Download the file tute1.csvfrom the book website, open it in Excel (or some other spreadsheet application), and review its contents. You should find four columns of information. Columns B through D each contain a quarterly series, labelled Sales, AdBudget and GDP. Sales contains the quarterly sales for a small company over the period 1981-2005. AdBudget is the advertising budget and GDP is the gross domestic product. All series have been adjusted for inflation.

  1. You can read the data into R with the following script:
tute1 <- readr::read_csv("tute1.csv", show_col_types = FALSE)
knit_table(tute1, caption='View tute1 Data')
View tute1 Data
Quarter Sales AdBudget GDP
3/1/81 1020.2 659.2 251.8
6/1/81 889.2 589.0 290.9
9/1/81 795.0 512.5 290.8
12/1/81 1003.9 614.1 292.4
3/1/82 1057.7 647.2 279.1
6/1/82 944.4 602.0 254.0
9/1/82 778.5 530.7 295.6
12/1/82 932.5 608.4 271.7
3/1/83 996.5 637.9 259.6
6/1/83 907.7 582.4 280.5
9/1/83 735.1 506.8 287.2
12/1/83 958.1 606.7 278.0
3/1/84 1034.1 658.7 256.8
6/1/84 992.8 614.9 271.0
9/1/84 791.7 489.9 300.9
12/1/84 914.2 586.5 289.8
3/1/85 1106.5 663.0 266.8
6/1/85 985.1 591.7 273.7
9/1/85 823.9 502.2 301.3
12/1/85 1025.1 616.4 285.6
3/1/86 1064.7 647.1 270.6
6/1/86 981.9 615.5 274.6
9/1/86 828.3 514.8 299.7
12/1/86 940.7 609.1 275.9
3/1/87 991.1 641.3 279.3
6/1/87 1021.2 620.2 290.8
9/1/87 796.7 511.2 295.6
12/1/87 986.6 621.3 271.9
3/1/88 1054.2 645.3 267.4
6/1/88 1018.7 616.0 281.0
9/1/88 815.6 503.2 309.0
12/1/88 1010.6 617.5 266.7
3/1/89 1071.5 642.8 283.5
6/1/89 954.0 585.6 282.3
9/1/89 822.9 520.6 289.2
12/1/89 867.5 608.6 270.7
3/1/90 1002.3 645.7 266.5
6/1/90 972.0 597.4 287.9
9/1/90 782.9 499.8 287.6
12/1/90 972.8 601.8 283.4
3/1/91 1108.0 650.8 266.4
6/1/91 943.7 588.3 292.3
9/1/91 806.1 491.6 330.6
12/1/91 954.2 603.3 286.2
3/1/92 1115.5 663.2 259.2
6/1/92 927.1 614.0 263.7
9/1/92 800.7 506.3 288.2
12/1/92 955.7 606.2 274.1
3/1/93 1049.8 639.5 287.1
6/1/93 886.0 585.9 285.5
9/1/93 786.4 492.2 303.7
12/1/93 991.3 610.4 275.6
3/1/94 1113.9 660.8 249.3
6/1/94 924.5 612.2 272.9
9/1/94 771.4 509.2 289.8
12/1/94 949.8 612.1 269.2
3/1/95 990.5 653.2 261.3
6/1/95 1071.4 605.3 292.9
9/1/95 854.1 506.6 304.6
12/1/95 929.8 597.4 276.3
3/1/96 959.6 635.2 268.2
6/1/96 991.1 611.6 293.5
9/1/96 832.9 503.8 311.1
12/1/96 1006.1 609.9 273.7
3/1/97 1040.7 645.2 267.5
6/1/97 1026.3 609.8 271.9
9/1/97 785.9 512.1 308.8
12/1/97 997.6 603.7 282.9
3/1/98 1055.0 639.4 268.4
6/1/98 925.6 601.6 271.4
9/1/98 805.6 497.0 292.1
12/1/98 934.1 602.8 287.6
3/1/99 1081.7 647.3 258.0
6/1/99 1062.3 612.5 282.9
9/1/99 798.8 492.2 295.0
12/1/99 1014.3 610.8 271.2
3/1/00 1049.5 646.5 275.4
6/1/00 961.7 603.3 284.0
9/1/00 793.4 503.8 300.9
12/1/00 872.3 598.3 277.4
3/1/01 1014.2 649.4 273.8
6/1/01 952.6 620.2 288.4
9/1/01 792.4 497.9 283.4
12/1/01 922.3 609.2 273.4
3/1/02 1055.9 665.9 271.5
6/1/02 906.2 600.4 283.6
9/1/02 811.2 502.3 290.6
12/1/02 1005.8 605.6 289.1
3/1/03 1013.8 647.6 282.2
6/1/03 905.6 583.5 285.6
9/1/03 957.3 502.5 304.0
12/1/03 1059.5 625.9 271.5
3/1/04 1090.6 648.7 263.9
6/1/04 998.9 610.7 288.3
9/1/04 866.6 519.1 290.2
12/1/04 1018.7 634.9 284.0
3/1/05 1112.5 663.1 270.9
6/1/05 997.4 583.3 294.7
9/1/05 826.8 508.6 292.2
12/1/05 992.6 634.2 255.1
  1. Convert the data to time series
mytimeseries <- tute1 |>
  # this line of code was added due to getting a date datatype error
  mutate(Quarter = as.Date(Quarter, format = "%m/%d/%y")) |>
  mutate(Quarter = yearquarter(Quarter)) |>
  as_tsibble(index = Quarter)
  1. Construct time series plots of each of the three series
mytimeseries |>
  pivot_longer(-Quarter) |>
  ggplot(aes(x = Quarter, y = value, colour = name)) +
  geom_line() +
  facet_grid(name ~ ., scales = "free_y")

Check what happens when you don’t include facet_grid().

mytimeseries |>
  pivot_longer(-Quarter) |>
  ggplot(aes(x = Quarter, y = value, colour = name)) +
  geom_line()

When you exclude facet_grid() from the plot, all three series occur on the same y-axis. Due to all three series having different ranges and variances, having them on the samey-axis makes it difficult to identify features between the data, including patterns, unusual observations, changes over time, and relationships between variables.

2.4

The USgas package contains data on the demand for natural gas in the US. a. Install the USgas package.

library(USgas)
  1. Create a tsibble from us_total with year as the index and state as the key.
us_gas = us_total |>
  as_tsibble(index=year, key=state)
knit_table(us_gas, caption='View us_total Data')
View us_total Data
year state y
1997 Alabama 324158
1998 Alabama 329134
1999 Alabama 337270
2000 Alabama 353614
2001 Alabama 332693
2002 Alabama 379343
2003 Alabama 350345
2004 Alabama 382367
2005 Alabama 353156
2006 Alabama 391093
2007 Alabama 418512
2008 Alabama 404157
2009 Alabama 454456
2010 Alabama 534779
2011 Alabama 598514
2012 Alabama 666712
2013 Alabama 615407
2014 Alabama 635323
2015 Alabama 681149
2016 Alabama 694881
2017 Alabama 661366
2018 Alabama 750188
2019 Alabama 729402
1997 Alaska 425393
1998 Alaska 434871
1999 Alaska 422816
2000 Alaska 427288
2001 Alaska 408960
2002 Alaska 419131
2003 Alaska 414234
2004 Alaska 406319
2005 Alaska 432972
2006 Alaska 373850
2007 Alaska 369967
2008 Alaska 341888
2009 Alaska 342261
2010 Alaska 333312
2011 Alaska 335458
2012 Alaska 343110
2013 Alaska 332298
2014 Alaska 328945
2015 Alaska 333602
2016 Alaska 330552
2017 Alaska 347725
2018 Alaska 355132
2019 Alaska 366476
1997 Arizona 134706
1998 Arizona 158355
1999 Arizona 165076
2000 Arizona 205235
2001 Arizona 240812
2002 Arizona 250734
2003 Arizona 272921
2004 Arizona 349622
2005 Arizona 321584
2006 Arizona 358069
2007 Arizona 392954
2008 Arizona 399188
2009 Arizona 369739
2010 Arizona 330914
2011 Arizona 288802
2012 Arizona 332068
2013 Arizona 332073
2014 Arizona 306715
2015 Arizona 351263
2016 Arizona 360576
2017 Arizona 321451
2018 Arizona 384753
2019 Arizona 468482
1997 Arkansas 260113
1998 Arkansas 266485
1999 Arkansas 252853
2000 Arkansas 251329
2001 Arkansas 227943
2002 Arkansas 242325
2003 Arkansas 246916
2004 Arkansas 215124
2005 Arkansas 213609
2006 Arkansas 233868
2007 Arkansas 226439
2008 Arkansas 234901
2009 Arkansas 244193
2010 Arkansas 271515
2011 Arkansas 284076
2012 Arkansas 296132
2013 Arkansas 282120
2014 Arkansas 268444
2015 Arkansas 291006
2016 Arkansas 309732
2017 Arkansas 311609
2018 Arkansas 360804
2019 Arkansas 360024
1997 California 2146211
1998 California 2309883
1999 California 2339521
2000 California 2508797
2001 California 2464565
2002 California 2273193
2003 California 2269405
2004 California 2406889
2005 California 2248256
2006 California 2315721
2007 California 2395674
2008 California 2405266
2009 California 2328504
2010 California 2273128
2011 California 2153186
2012 California 2403494
2013 California 2415571
2014 California 2339392
2015 California 2301217
2016 California 2172889
2017 California 2116902
2018 California 2137920
2019 California 2154030
1997 Colorado 314486
1998 Colorado 330259
1999 Colorado 333085
2000 Colorado 367920
2001 Colorado 463738
2002 Colorado 459397
2003 Colorado 436253
2004 Colorado 440378
2005 Colorado 470321
2006 Colorado 450832
2007 Colorado 504775
2008 Colorado 504783
2009 Colorado 523726
2010 Colorado 501350
2011 Colorado 466680
2012 Colorado 443750
2013 Colorado 467798
2014 Colorado 478987
2015 Colorado 466906
2016 Colorado 441018
2017 Colorado 438137
2018 Colorado 485735
2019 Colorado 520139
1997 Connecticut 144708
1998 Connecticut 131497
1999 Connecticut 152237
2000 Connecticut 159712
2001 Connecticut 146278
2002 Connecticut 177587
2003 Connecticut 154075
2004 Connecticut 162642
2005 Connecticut 168067
2006 Connecticut 172682
2007 Connecticut 180181
2008 Connecticut 166801
2009 Connecticut 185056
2010 Connecticut 199426
2011 Connecticut 230036
2012 Connecticut 229156
2013 Connecticut 234475
2014 Connecticut 235859
2015 Connecticut 254065
2016 Connecticut 247958
2017 Connecticut 239818
2018 Connecticut 277931
2019 Connecticut 283408
1997 Delaware 46511
1998 Delaware 40809
1999 Delaware 56013
2000 Delaware 48387
2001 Delaware 50113
2002 Delaware 52216
2003 Delaware 46177
2004 Delaware 48057
2005 Delaware 46904
2006 Delaware 43190
2007 Delaware 48155
2008 Delaware 48162
2009 Delaware 50148
2010 Delaware 54825
2011 Delaware 79715
2012 Delaware 101676
2013 Delaware 95978
2014 Delaware 101379
2015 Delaware 102693
2016 Delaware 108562
2017 Delaware 98966
2018 Delaware 95516
2019 Delaware 89214
1997 District of Columbia 34105
1998 District of Columbia 30409
1999 District of Columbia 32281
2000 District of Columbia 33468
2001 District of Columbia 29802
2002 District of Columbia 32898
2003 District of Columbia 32814
2004 District of Columbia 32227
2005 District of Columbia 32085
2006 District of Columbia 29049
2007 District of Columbia 32966
2008 District of Columbia 31880
2009 District of Columbia 33177
2010 District of Columbia 33251
2011 District of Columbia 32862
2012 District of Columbia 28561
2013 District of Columbia 32743
2014 District of Columbia 33848
2015 District of Columbia 32237
2016 District of Columbia 28888
2017 District of Columbia 29457
2018 District of Columbia 31490
2019 District of Columbia 30544
1999 Federal Offshore – Gulf of Mexico 0
2000 Federal Offshore – Gulf of Mexico 0
2001 Federal Offshore – Gulf of Mexico 0
2002 Federal Offshore – Gulf of Mexico 109277
2003 Federal Offshore – Gulf of Mexico 98372
2004 Federal Offshore – Gulf of Mexico 90025
2005 Federal Offshore – Gulf of Mexico 78139
2006 Federal Offshore – Gulf of Mexico 102242
2007 Federal Offshore – Gulf of Mexico 115528
2008 Federal Offshore – Gulf of Mexico 102389
2009 Federal Offshore – Gulf of Mexico 103976
2010 Federal Offshore – Gulf of Mexico 108490
2011 Federal Offshore – Gulf of Mexico 101217
2012 Federal Offshore – Gulf of Mexico 93985
2013 Federal Offshore – Gulf of Mexico 95207
2014 Federal Offshore – Gulf of Mexico 93814
2015 Federal Offshore – Gulf of Mexico 95492
2016 Federal Offshore – Gulf of Mexico 95832
2017 Federal Offshore – Gulf of Mexico 94379
2018 Federal Offshore – Gulf of Mexico 94178
2019 Federal Offshore – Gulf of Mexico 94298
1997 Florida 522116
1998 Florida 503844
1999 Florida 559366
2000 Florida 541847
2001 Florida 543143
2002 Florida 689337
2003 Florida 689986
2004 Florida 734178
2005 Florida 778209
2006 Florida 891611
2007 Florida 917244
2008 Florida 942699
2009 Florida 1055340
2010 Florida 1158452
2011 Florida 1217689
2012 Florida 1328463
2013 Florida 1225676
2014 Florida 1214531
2015 Florida 1345790
2016 Florida 1382558
2017 Florida 1387960
2018 Florida 1477160
2019 Florida 1545434
1997 Georgia 371376
1998 Georgia 368579
1999 Georgia 337576
2000 Georgia 413845
2001 Georgia 351109
2002 Georgia 383546
2003 Georgia 379761
2004 Georgia 394986
2005 Georgia 412560
2006 Georgia 420469
2007 Georgia 441107
2008 Georgia 425043
2009 Georgia 462799
2010 Georgia 530030
2011 Georgia 522897
2012 Georgia 615771
2013 Georgia 625283
2014 Georgia 652408
2015 Georgia 694399
2016 Georgia 706688
2017 Georgia 689501
2018 Georgia 738986
2019 Georgia 753735
1997 Hawaii 2894
1998 Hawaii 2654
1999 Hawaii 3115
2000 Hawaii 2841
2001 Hawaii 2818
2002 Hawaii 2734
2003 Hawaii 2732
2004 Hawaii 2774
2005 Hawaii 2795
2006 Hawaii 2783
2007 Hawaii 2850
2008 Hawaii 2702
2009 Hawaii 2607
2010 Hawaii 2627
2011 Hawaii 2619
2012 Hawaii 2689
2013 Hawaii 2855
2014 Hawaii 2916
2015 Hawaii 2924
2016 Hawaii 3040
2017 Hawaii 3106
2018 Hawaii 3282
2019 Hawaii 3277
1997 Idaho 68669
1998 Idaho 69277
1999 Idaho 70672
2000 Idaho 72697
2001 Idaho 80279
2002 Idaho 71481
2003 Idaho 69868
2004 Idaho 75335
2005 Idaho 74540
2006 Idaho 75709
2007 Idaho 81937
2008 Idaho 88515
2009 Idaho 85197
2010 Idaho 83326
2011 Idaho 82544
2012 Idaho 89004
2013 Idaho 104783
2014 Idaho 92046
2015 Idaho 104730
2016 Idaho 106306
2017 Idaho 111334
2018 Idaho 111700
2019 Idaho 127638
1997 Illinois 1077139
1998 Illinois 957254
1999 Illinois 1004281
2000 Illinois 1030604
2001 Illinois 951616
2002 Illinois 1049878
2003 Illinois 998486
2004 Illinois 953207
2005 Illinois 969642
2006 Illinois 893997
2007 Illinois 965591
2008 Illinois 1000501
2009 Illinois 956068
2010 Illinois 966678
2011 Illinois 986867
2012 Illinois 940367
2013 Illinois 1056826
2014 Illinois 1093931
2015 Illinois 993548
2016 Illinois 1024186
2017 Illinois 1017772
2018 Illinois 1108592
2019 Illinois 1134722
1997 Indiana 556624
1998 Indiana 521748
1999 Indiana 556932
2000 Indiana 570558
2001 Indiana 501711
2002 Indiana 539034
2003 Indiana 527037
2004 Indiana 526701
2005 Indiana 531111
2006 Indiana 496303
2007 Indiana 535796
2008 Indiana 551424
2009 Indiana 506944
2010 Indiana 573866
2011 Indiana 630669
2012 Indiana 649921
2013 Indiana 672751
2014 Indiana 713416
2015 Indiana 718725
2016 Indiana 754276
2017 Indiana 720453
2018 Indiana 854024
2019 Indiana 894471
1997 Iowa 254489
1998 Iowa 232057
1999 Iowa 230691
2000 Iowa 232565
2001 Iowa 224336
2002 Iowa 226457
2003 Iowa 230161
2004 Iowa 226819
2005 Iowa 241340
2006 Iowa 238454
2007 Iowa 293274
2008 Iowa 325772
2009 Iowa 315186
2010 Iowa 311075
2011 Iowa 306909
2012 Iowa 295183
2013 Iowa 326140
2014 Iowa 329385
2015 Iowa 317821
2016 Iowa 330094
2017 Iowa 391129
2018 Iowa 443174
2019 Iowa 442873
1997 Kansas 338231
1998 Kansas 326674
1999 Kansas 302932
2000 Kansas 312369
2001 Kansas 272500
2002 Kansas 304992
2003 Kansas 281346
2004 Kansas 256779
2005 Kansas 255123
2006 Kansas 264253
2007 Kansas 286538
2008 Kansas 282904
2009 Kansas 286973
2010 Kansas 275184
2011 Kansas 279724
2012 Kansas 262316
2013 Kansas 283177
2014 Kansas 284651
2015 Kansas 270938
2016 Kansas 267315
2017 Kansas 269919
2018 Kansas 310028
2019 Kansas 306050
1997 Kentucky 227931
1998 Kentucky 205129
1999 Kentucky 218399
2000 Kentucky 225168
2001 Kentucky 208974
2002 Kentucky 227920
2003 Kentucky 223226
2004 Kentucky 225470
2005 Kentucky 234080
2006 Kentucky 211049
2007 Kentucky 229799
2008 Kentucky 225295
2009 Kentucky 206833
2010 Kentucky 232099
2011 Kentucky 223034
2012 Kentucky 225924
2013 Kentucky 229983
2014 Kentucky 255434
2015 Kentucky 270958
2016 Kentucky 271845
2017 Kentucky 283678
2018 Kentucky 340125
2019 Kentucky 336191
1997 Louisiana 1661061
1998 Louisiana 1569190
1999 Louisiana 1495478
2000 Louisiana 1536725
2001 Louisiana 1219013
2002 Louisiana 1341444
2003 Louisiana 1233505
2004 Louisiana 1281428
2005 Louisiana 1254370
2006 Louisiana 1217871
2007 Louisiana 1289421
2008 Louisiana 1238661
2009 Louisiana 1189744
2010 Louisiana 1354641
2011 Louisiana 1420264
2012 Louisiana 1482343
2013 Louisiana 1396261
2014 Louisiana 1423424
2015 Louisiana 1470354
2016 Louisiana 1591882
2017 Louisiana 1593181
2018 Louisiana 1738734
2019 Louisiana 1861894
1997 Maine 6290
1998 Maine 5716
1999 Maine 6572
2000 Maine 44779
2001 Maine 95733
2002 Maine 101536
2003 Maine 70832
2004 Maine 72565
2005 Maine 57835
2006 Maine 49605
2007 Maine 63183
2008 Maine 70146
2009 Maine 70334
2010 Maine 77575
2011 Maine 71690
2012 Maine 68266
2013 Maine 64091
2014 Maine 60663
2015 Maine 52777
2016 Maine 53128
2017 Maine 43810
2018 Maine 46464
2019 Maine 44484
1997 Maryland 212017
1998 Maryland 188552
1999 Maryland 196350
2000 Maryland 212133
2001 Maryland 178376
2002 Maryland 196276
2003 Maryland 197024
2004 Maryland 194725
2005 Maryland 202509
2006 Maryland 182294
2007 Maryland 201053
2008 Maryland 196067
2009 Maryland 196510
2010 Maryland 212020
2011 Maryland 193986
2012 Maryland 208946
2013 Maryland 197356
2014 Maryland 207103
2015 Maryland 215005
2016 Maryland 219024
2017 Maryland 222881
2018 Maryland 300637
2019 Maryland 300876
1997 Massachusetts 402629
1998 Massachusetts 358846
1999 Massachusetts 344790
2000 Massachusetts 343314
2001 Massachusetts 349103
2002 Massachusetts 393194
2003 Massachusetts 403991
2004 Massachusetts 372532
2005 Massachusetts 378068
2006 Massachusetts 370664
2007 Massachusetts 408704
2008 Massachusetts 406719
2009 Massachusetts 395852
2010 Massachusetts 432297
2011 Massachusetts 449194
2012 Massachusetts 416350
2013 Massachusetts 421001
2014 Massachusetts 421671
2015 Massachusetts 444332
2016 Massachusetts 427946
2017 Massachusetts 448996
2018 Massachusetts 438577
2019 Massachusetts 433774
1997 Michigan 994342
1998 Michigan 876444
1999 Michigan 951143
2000 Michigan 963136
2001 Michigan 906001
2002 Michigan 966354
2003 Michigan 924819
2004 Michigan 916629
2005 Michigan 913827
2006 Michigan 803336
2007 Michigan 798126
2008 Michigan 779602
2009 Michigan 735340
2010 Michigan 746748
2011 Michigan 776466
2012 Michigan 790642
2013 Michigan 814635
2014 Michigan 861755
2015 Michigan 844801
2016 Michigan 890324
2017 Michigan 870756
2018 Michigan 965538
2019 Michigan 1002237
1997 Minnesota 354092
1998 Minnesota 330513
1999 Minnesota 344591
2000 Minnesota 362025
2001 Minnesota 340911
2002 Minnesota 371583
2003 Minnesota 371261
2004 Minnesota 359898
2005 Minnesota 367825
2006 Minnesota 352570
2007 Minnesota 388335
2008 Minnesota 425352
2009 Minnesota 394136
2010 Minnesota 422968
2011 Minnesota 420770
2012 Minnesota 422263
2013 Minnesota 467874
2014 Minnesota 474520
2015 Minnesota 431315
2016 Minnesota 449783
2017 Minnesota 451979
2018 Minnesota 490169
2019 Minnesota 509061
1997 Mississippi 255475
1998 Mississippi 241342
1999 Mississippi 306733
2000 Mississippi 300652
2001 Mississippi 332589
2002 Mississippi 343890
2003 Mississippi 265842
2004 Mississippi 282051
2005 Mississippi 301663
2006 Mississippi 307305
2007 Mississippi 364067
2008 Mississippi 355006
2009 Mississippi 364323
2010 Mississippi 438733
2011 Mississippi 433538
2012 Mississippi 494016
2013 Mississippi 420594
2014 Mississippi 427584
2015 Mississippi 521355
2016 Mississippi 544464
2017 Mississippi 526862
2018 Mississippi 576888
2019 Mississippi 570154
1997 Missouri 283294
1998 Missouri 258652
1999 Missouri 265798
2000 Missouri 284763
2001 Missouri 283793
2002 Missouri 275629
2003 Missouri 262529
2004 Missouri 263945
2005 Missouri 268040
2006 Missouri 252697
2007 Missouri 272536
2008 Missouri 296058
2009 Missouri 264867
2010 Missouri 280181
2011 Missouri 272583
2012 Missouri 255875
2013 Missouri 276967
2014 Missouri 297087
2015 Missouri 267673
2016 Missouri 267170
2017 Missouri 261993
2018 Missouri 322805
2019 Missouri 316378
1997 Montana 59851
1998 Montana 59840
1999 Montana 62129
2000 Montana 67955
2001 Montana 65051
2002 Montana 69532
2003 Montana 68473
2004 Montana 66829
2005 Montana 68355
2006 Montana 73879
2007 Montana 73822
2008 Montana 76422
2009 Montana 75802
2010 Montana 72025
2011 Montana 78217
2012 Montana 73399
2013 Montana 79670
2014 Montana 78110
2015 Montana 75042
2016 Montana 75037
2017 Montana 80036
2018 Montana 87034
2019 Montana 88394
1997 Nebraska 132221
1998 Nebraska 130730
1999 Nebraska 121487
2000 Nebraska 126962
2001 Nebraska 121984
2002 Nebraska 120333
2003 Nebraska 118922
2004 Nebraska 115011
2005 Nebraska 119070
2006 Nebraska 129885
2007 Nebraska 150808
2008 Nebraska 171005
2009 Nebraska 163474
2010 Nebraska 168944
2011 Nebraska 171777
2012 Nebraska 158757
2013 Nebraska 173376
2014 Nebraska 172837
2015 Nebraska 161189
2016 Nebraska 163362
2017 Nebraska 166286
2018 Nebraska 185949
2019 Nebraska 185260
1997 Nevada 132128
1998 Nevada 148539
1999 Nevada 154689
2000 Nevada 189170
2001 Nevada 176835
2002 Nevada 176596
2003 Nevada 185846
2004 Nevada 214984
2005 Nevada 227149
2006 Nevada 249608
2007 Nevada 254406
2008 Nevada 264596
2009 Nevada 275468
2010 Nevada 259251
2011 Nevada 249971
2012 Nevada 273502
2013 Nevada 272965
2014 Nevada 253290
2015 Nevada 300002
2016 Nevada 304181
2017 Nevada 293849
2018 Nevada 299783
2019 Nevada 302373
1997 New Hampshire 20848
1998 New Hampshire 19127
1999 New Hampshire 20313
2000 New Hampshire 24950
2001 New Hampshire 23398
2002 New Hampshire 24901
2003 New Hampshire 54147
2004 New Hampshire 61172
2005 New Hampshire 70484
2006 New Hampshire 62549
2007 New Hampshire 62132
2008 New Hampshire 71179
2009 New Hampshire 59950
2010 New Hampshire 60378
2011 New Hampshire 69978
2012 New Hampshire 72032
2013 New Hampshire 54028
2014 New Hampshire 57018
2015 New Hampshire 68682
2016 New Hampshire 57957
2017 New Hampshire 52071
2018 New Hampshire 49888
2019 New Hampshire 53624
1997 New Jersey 717011
1998 New Jersey 679619
1999 New Jersey 715630
2000 New Jersey 605275
2001 New Jersey 564923
2002 New Jersey 598602
2003 New Jersey 612890
2004 New Jersey 620806
2005 New Jersey 602388
2006 New Jersey 547206
2007 New Jersey 618965
2008 New Jersey 614908
2009 New Jersey 620790
2010 New Jersey 654458
2011 New Jersey 660743
2012 New Jersey 652060
2013 New Jersey 682247
2014 New Jersey 773221
2015 New Jersey 745789
2016 New Jersey 762958
2017 New Jersey 706589
2018 New Jersey 770284
2019 New Jersey 766824
1997 New Mexico 256464
1998 New Mexico 245823
1999 New Mexico 236264
2000 New Mexico 266469
2001 New Mexico 266283
2002 New Mexico 235098
2003 New Mexico 221021
2004 New Mexico 223575
2005 New Mexico 220717
2006 New Mexico 223636
2007 New Mexico 234236
2008 New Mexico 246665
2009 New Mexico 241194
2010 New Mexico 241137
2011 New Mexico 246418
2012 New Mexico 243961
2013 New Mexico 245502
2014 New Mexico 247637
2015 New Mexico 250518
2016 New Mexico 247761
2017 New Mexico 239305
2018 New Mexico 271547
2019 New Mexico 296753
1997 New York 1324164
1998 New York 1232473
1999 New York 1274162
2000 New York 1244746
2001 New York 1171898
2002 New York 1199632
2003 New York 1101618
2004 New York 1098056
2005 New York 1080215
2006 New York 1097160
2007 New York 1187059
2008 New York 1180356
2009 New York 1142625
2010 New York 1198127
2011 New York 1217324
2012 New York 1223036
2013 New York 1273263
2014 New York 1349203
2015 New York 1353385
2016 New York 1296270
2017 New York 1237311
2018 New York 1350443
2019 New York 1312031
1997 North Carolina 215634
1998 North Carolina 214092
1999 North Carolina 217159
2000 North Carolina 233714
2001 North Carolina 207108
2002 North Carolina 235376
2003 North Carolina 218642
2004 North Carolina 224796
2005 North Carolina 229715
2006 North Carolina 223032
2007 North Carolina 237354
2008 North Carolina 243090
2009 North Carolina 247047
2010 North Carolina 304148
2011 North Carolina 307804
2012 North Carolina 363945
2013 North Carolina 440175
2014 North Carolina 452780
2015 North Carolina 498576
2016 North Carolina 522002
2017 North Carolina 502567
2018 North Carolina 582418
2019 North Carolina 556490
1997 North Dakota 56179
1998 North Dakota 49541
1999 North Dakota 56418
2000 North Dakota 56528
2001 North Dakota 60819
2002 North Dakota 66726
2003 North Dakota 60907
2004 North Dakota 59986
2005 North Dakota 53050
2006 North Dakota 53336
2007 North Dakota 59453
2008 North Dakota 63097
2009 North Dakota 54564
2010 North Dakota 66395
2011 North Dakota 72463
2012 North Dakota 72740
2013 North Dakota 81593
2014 North Dakota 86881
2015 North Dakota 97725
2016 North Dakota 102322
2017 North Dakota 109440
2018 North Dakota 126325
2019 North Dakota 134722
1997 Ohio 897693
1998 Ohio 811384
1999 Ohio 841966
2000 Ohio 890962
2001 Ohio 804243
2002 Ohio 830955
2003 Ohio 848388
2004 Ohio 825753
2005 Ohio 825961
2006 Ohio 742359
2007 Ohio 806350
2008 Ohio 792247
2009 Ohio 740925
2010 Ohio 784293
2011 Ohio 823548
2012 Ohio 842959
2013 Ohio 912403
2014 Ohio 1002345
2015 Ohio 966492
2016 Ohio 928492
2017 Ohio 948324
2018 Ohio 1162745
2019 Ohio 1179077
1997 Oklahoma 567050
1998 Oklahoma 575855
1999 Oklahoma 538329
2000 Oklahoma 538563
2001 Oklahoma 491458
2002 Oklahoma 508298
2003 Oklahoma 540103
2004 Oklahoma 538576
2005 Oklahoma 582536
2006 Oklahoma 624400
2007 Oklahoma 658379
2008 Oklahoma 687989
2009 Oklahoma 659305
2010 Oklahoma 675727
2011 Oklahoma 655919
2012 Oklahoma 691661
2013 Oklahoma 658569
2014 Oklahoma 642309
2015 Oklahoma 679457
2016 Oklahoma 701776
2017 Oklahoma 664233
2018 Oklahoma 807023
2019 Oklahoma 835139
1997 Oregon 185069
1998 Oregon 229403
1999 Oregon 235009
2000 Oregon 224888
2001 Oregon 229665
2002 Oregon 202164
2003 Oregon 212556
2004 Oregon 234997
2005 Oregon 232562
2006 Oregon 222608
2007 Oregon 251927
2008 Oregon 268484
2009 Oregon 248864
2010 Oregon 239325
2011 Oregon 199419
2012 Oregon 215830
2013 Oregon 240418
2014 Oregon 220090
2015 Oregon 234634
2016 Oregon 235912
2017 Oregon 247206
2018 Oregon 255713
2019 Oregon 288976
1997 Pennsylvania 706230
1998 Pennsylvania 644017
1999 Pennsylvania 688740
2000 Pennsylvania 702847
2001 Pennsylvania 634794
2002 Pennsylvania 675583
2003 Pennsylvania 689992
2004 Pennsylvania 696175
2005 Pennsylvania 691591
2006 Pennsylvania 659754
2007 Pennsylvania 752401
2008 Pennsylvania 749884
2009 Pennsylvania 809707
2010 Pennsylvania 879365
2011 Pennsylvania 965742
2012 Pennsylvania 1037979
2013 Pennsylvania 1121696
2014 Pennsylvania 1244371
2015 Pennsylvania 1255621
2016 Pennsylvania 1301000
2017 Pennsylvania 1350245
2018 Pennsylvania 1460456
2019 Pennsylvania 1612589
1997 Rhode Island 117707
1998 Rhode Island 130751
1999 Rhode Island 118001
2000 Rhode Island 88419
2001 Rhode Island 95607
2002 Rhode Island 87805
2003 Rhode Island 78456
2004 Rhode Island 72609
2005 Rhode Island 80764
2006 Rhode Island 77204
2007 Rhode Island 87972
2008 Rhode Island 89256
2009 Rhode Island 92743
2010 Rhode Island 94110
2011 Rhode Island 100455
2012 Rhode Island 95476
2013 Rhode Island 85537
2014 Rhode Island 88886
2015 Rhode Island 93886
2016 Rhode Island 85977
2017 Rhode Island 92061
2018 Rhode Island 101796
2019 Rhode Island 99301
1997 South Carolina 153917
1998 South Carolina 159458
1999 South Carolina 162926
2000 South Carolina 160436
2001 South Carolina 141785
2002 South Carolina 184803
2003 South Carolina 146641
2004 South Carolina 163787
2005 South Carolina 172032
2006 South Carolina 174806
2007 South Carolina 175701
2008 South Carolina 170077
2009 South Carolina 190928
2010 South Carolina 220235
2011 South Carolina 229497
2012 South Carolina 244850
2013 South Carolina 232297
2014 South Carolina 230525
2015 South Carolina 275751
2016 South Carolina 275946
2017 South Carolina 278768
2018 South Carolina 330362
2019 South Carolina 337310
1997 South Dakota 36115
1998 South Dakota 33042
1999 South Dakota 35794
2000 South Dakota 37939
2001 South Dakota 37077
2002 South Dakota 41577
2003 South Dakota 43881
2004 South Dakota 41679
2005 South Dakota 42555
2006 South Dakota 40739
2007 South Dakota 53938
2008 South Dakota 65258
2009 South Dakota 66185
2010 South Dakota 72563
2011 South Dakota 73605
2012 South Dakota 70238
2013 South Dakota 81986
2014 South Dakota 80613
2015 South Dakota 79099
2016 South Dakota 80513
2017 South Dakota 80890
2018 South Dakota 89464
2019 South Dakota 91362
1997 Tennessee 282395
1998 Tennessee 279070
1999 Tennessee 278841
2000 Tennessee 270658
2001 Tennessee 255990
2002 Tennessee 255515
2003 Tennessee 257315
2004 Tennessee 231133
2005 Tennessee 230338
2006 Tennessee 221626
2007 Tennessee 221118
2008 Tennessee 229935
2009 Tennessee 216945
2010 Tennessee 257443
2011 Tennessee 264231
2012 Tennessee 277127
2013 Tennessee 279441
2014 Tennessee 305633
2015 Tennessee 313379
2016 Tennessee 326546
2017 Tennessee 321644
2018 Tennessee 392161
2019 Tennessee 402277
1997 Texas 4116722
1998 Texas 4205459
1999 Texas 4009689
2000 Texas 4421777
2001 Texas 4252152
2002 Texas 4303831
2003 Texas 4050632
2004 Texas 3908243
2005 Texas 3503636
2006 Texas 3432236
2007 Texas 3516706
2008 Texas 3546804
2009 Texas 3387341
2010 Texas 3574398
2011 Texas 3693905
2012 Texas 3850331
2013 Texas 4021851
2014 Texas 3928277
2015 Texas 4113608
2016 Texas 4020915
2017 Texas 3867275
2018 Texas 4464219
2019 Texas 4619800
1949 U.S. 4971152
1950 U.S. 5766542
1951 U.S. 6810162
1952 U.S. 7294320
1953 U.S. 7639270
1954 U.S. 8048504
1955 U.S. 8693657
1956 U.S. 9288865
1957 U.S. 9846139
1958 U.S. 10302608
1959 U.S. 11321181
1960 U.S. 11966537
1961 U.S. 12489268
1962 U.S. 13266513
1963 U.S. 13970229
1964 U.S. 14813808
1965 U.S. 15279716
1966 U.S. 16452403
1967 U.S. 17388360
1968 U.S. 18632062
1969 U.S. 20056240
1970 U.S. 21139386
1971 U.S. 21793454
1972 U.S. 22101451
1973 U.S. 22049363
1974 U.S. 21223133
1975 U.S. 19537593
1976 U.S. 19946496
1977 U.S. 19520581
1978 U.S. 19627478
1979 U.S. 20240761
1980 U.S. 19877293
1981 U.S. 19403858
1982 U.S. 18001055
1983 U.S. 16834912
1984 U.S. 17950527
1985 U.S. 17280943
1986 U.S. 16221296
1987 U.S. 17210809
1988 U.S. 18029585
1989 U.S. 19118997
1990 U.S. 19173556
1991 U.S. 19562067
1992 U.S. 20228228
1993 U.S. 20789842
1994 U.S. 21247098
1995 U.S. 22206889
1996 U.S. 22609080
1997 U.S. 22737342
1998 U.S. 22245956
1999 U.S. 22405151
2000 U.S. 23333121
2001 U.S. 22238624
2002 U.S. 23027021
2003 U.S. 22276502
2004 U.S. 22402546
2005 U.S. 22014434
2006 U.S. 21699071
2007 U.S. 23103793
2008 U.S. 23277008
2009 U.S. 22910078
2010 U.S. 24086797
2011 U.S. 24477425
2012 U.S. 25538487
2013 U.S. 26155071
2014 U.S. 26593375
2015 U.S. 27243858
2016 U.S. 27444220
2017 U.S. 27139699
2018 U.S. 30138930
2019 U.S. 31099061
2020 U.S. 30482049
1997 Utah 165253
1998 Utah 169776
1999 Utah 159889
2000 Utah 164557
2001 Utah 159299
2002 Utah 163379
2003 Utah 154125
2004 Utah 155891
2005 Utah 160275
2006 Utah 187399
2007 Utah 219700
2008 Utah 224188
2009 Utah 214220
2010 Utah 219213
2011 Utah 222227
2012 Utah 223039
2013 Utah 247285
2014 Utah 241737
2015 Utah 232612
2016 Utah 240114
2017 Utah 221834
2018 Utah 244058
2019 Utah 264046
1997 Vermont 8061
1998 Vermont 7735
1999 Vermont 8033
2000 Vermont 10426
2001 Vermont 7919
2002 Vermont 8367
2003 Vermont 8400
2004 Vermont 8685
2005 Vermont 8372
2006 Vermont 8056
2007 Vermont 8867
2008 Vermont 8624
2009 Vermont 8638
2010 Vermont 8443
2011 Vermont 8611
2012 Vermont 8191
2013 Vermont 9602
2014 Vermont 10677
2015 Vermont 11950
2016 Vermont 12094
2017 Vermont 11926
2018 Vermont 13742
2019 Vermont 13866
1997 Virginia 248960
1998 Virginia 260332
1999 Virginia 276793
2000 Virginia 268770
2001 Virginia 237853
2002 Virginia 258202
2003 Virginia 262970
2004 Virginia 277434
2005 Virginia 299746
2006 Virginia 274175
2007 Virginia 319913
2008 Virginia 299364
2009 Virginia 319134
2010 Virginia 375421
2011 Virginia 373444
2012 Virginia 410106
2013 Virginia 418506
2014 Virginia 419705
2015 Virginia 500477
2016 Virginia 543343
2017 Virginia 566676
2018 Virginia 634162
2019 Virginia 684597
1997 Washington 256366
1998 Washington 290229
1999 Washington 287302
2000 Washington 286653
2001 Washington 312114
2002 Washington 233716
2003 Washington 249599
2004 Washington 262485
2005 Washington 264754
2006 Washington 263395
2007 Washington 272613
2008 Washington 298140
2009 Washington 310428
2010 Washington 285726
2011 Washington 264589
2012 Washington 264540
2013 Washington 318292
2014 Washington 306675
2015 Washington 307735
2016 Washington 301418
2017 Washington 324882
2018 Washington 307985
2019 Washington 345210
1997 West Virginia 159504
1998 West Virginia 142860
1999 West Virginia 139961
2000 West Virginia 147854
2001 West Virginia 141090
2002 West Virginia 146455
2003 West Virginia 126986
2004 West Virginia 122267
2005 West Virginia 117136
2006 West Virginia 113084
2007 West Virginia 115974
2008 West Virginia 111480
2009 West Virginia 109652
2010 West Virginia 113179
2011 West Virginia 115361
2012 West Virginia 129753
2013 West Virginia 142082
2014 West Virginia 165341
2015 West Virginia 174165
2016 West Virginia 171825
2017 West Virginia 184025
2018 West Virginia 202934
2019 West Virginia 218282
1997 Wisconsin 400651
1998 Wisconsin 368022
1999 Wisconsin 380560
2000 Wisconsin 393601
2001 Wisconsin 359784
2002 Wisconsin 385310
2003 Wisconsin 394711
2004 Wisconsin 383316
2005 Wisconsin 410250
2006 Wisconsin 372462
2007 Wisconsin 398370
2008 Wisconsin 409377
2009 Wisconsin 387066
2010 Wisconsin 372898
2011 Wisconsin 393734
2012 Wisconsin 402656
2013 Wisconsin 442544
2014 Wisconsin 463186
2015 Wisconsin 457743
2016 Wisconsin 482233
2017 Wisconsin 487732
2018 Wisconsin 543025
2019 Wisconsin 576650
1997 Wyoming 100950
1998 Wyoming 109188
1999 Wyoming 96726
2000 Wyoming 101314
2001 Wyoming 98569
2002 Wyoming 112872
2003 Wyoming 115358
2004 Wyoming 107060
2005 Wyoming 108314
2006 Wyoming 108481
2007 Wyoming 140912
2008 Wyoming 142705
2009 Wyoming 142793
2010 Wyoming 150106
2011 Wyoming 156455
2012 Wyoming 153333
2013 Wyoming 149820
2014 Wyoming 136796
2015 Wyoming 119265
2016 Wyoming 123351
2017 Wyoming 149405
2018 Wyoming 165384
2019 Wyoming 154836
  1. Plot the annual natural gas consumption by state for the New England area (comprising the states of Maine, Vermont, New Hampshire, Massachusetts, Connecticut and Rhode Island).
us_gas |>
  filter(state %in% c('Maine', 'Vermont', 'New Hampshire', 'Massachusetts', 'Connecticut', 'Rhode Island')) |>
  autoplot(y) +
  labs(y='MMcf', title='New England Area States Annual Demand for Natural Gas') +
  scale_y_continuous(labels = scales::comma) +
  theme_minimal()

2.5

  1. Download tourism.xlsx from the book website and read it into R using readxl::read_excel().
tour_data = readxl::read_excel('tourism.xlsx')
  1. Create a tsibble which is identical to the tourism tsibble from the tsibble package.
knit_table(
  tribble(
    ~Index, ~Key_Variables,
    index(tsibble::tourism),
    key_vars(tsibble::tourism)
    ),
  'tourism tsibble properties from the tsibble package'
)
tourism tsibble properties from the tsibble package
Index Key_Variables
Quarter Region , State , Purpose 
# create identical tsibble
keys = c('Region', 'State', 'Purpose')
tour = tour_data|>
  mutate(Quarter = yearquarter(Quarter)) |>
  as_tsibble(index=Quarter, key=all_of(keys))

knit_table(
  tribble(
    ~Index, ~Key_Variables,
    index(tour),
    key_vars(tour)
    ),
  'tourism tsibble properties from the tourism.xlsx download'
)
tourism tsibble properties from the tourism.xlsx download
Index Key_Variables
Quarter Region , State , Purpose
  1. Find what combination of Region and Purpose had the maximum number of overnight trips on average.
tour_agg = tour |>
  group_by(Region, Purpose) |>
  mutate(Avg_Trips = mean(Trips)) |>
  ungroup() |>
  filter(Avg_Trips == max(Avg_Trips)) |>
  distinct(Region, Purpose, Avg_Trips)
knit_table(tour_agg, 'Region and Purpose with the maximum number of overnight trips on average')
Region and Purpose with the maximum number of overnight trips on average
Region Purpose Avg_Trips
Sydney Visiting 747.27
  1. Create a new tsibble which combines the Purposes and Regions, and just has total trips by State.
tour_state = tour |>
  group_by(State) |>
  mutate(Trips = sum(Trips)) |>
  distinct(State, Trips)
knit_table(tour_state, 'Total Australian Domestic Overnight Trips (thousands) by State')
Total Australian Domestic Overnight Trips (thousands) by State
State Trips
South Australia 118151.35
Northern Territory 28613.68
Western Australia 147819.65
Victoria 390462.91
New South Wales 557367.43
Queensland 386642.91
ACT 41006.59
Tasmania 54137.09

2.8

Use the following graphics functions: autoplot(), gg_season(), gg_subseries(), gg_lag(), ACF() and explore features from the following time series: “Total Private” Employed from us_employment, Bricks from aus_production, Hare from pelt, “H02” Cost from PBS, and Barrels from us_gasoline.

  • Can you spot any seasonality, cyclicity and trend?
  • What do you learn about the seriesz
  • What can you say about the seasonal patterns?
  • Can you identify any unusual years?
ts_graphics <- function(df, y, y_lable, per=NULL) {
  p1 = df |>
    autoplot({{y}}) +
    ylab(y_lable)
  
  p2 = df |>
    gg_season({{y}}, per) +
    ylab(y_lable)

  p3 = df |>
    gg_subseries({{y}}) +
    ylab(y_lable)

  p4 = df |>
    ggtime::gg_lag({{y}}, geom = "point") +
    labs(x = "lag(Beer, k)")
  
  p5 = df |>
    ACF({{y}}) |>
    autoplot()
  
  return(c(p1, p2, p3, p4, p5))
}
# ?us_employment
tp_us_employment = us_employment|>
  filter(
    Title == 'Total Private',
    year(Month) >= 1980
  )

ts_graphics(tp_us_employment, Employed, 'US Employment', 'year')
## Warning: `gg_season()` was deprecated in feasts 0.4.2.
## ℹ Please use `ggtime::gg_season()` instead.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.
## Warning: `gg_subseries()` was deprecated in feasts 0.4.2.
## ℹ Please use `ggtime::gg_subseries()` instead.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.
## Registered S3 methods overwritten by 'ggtime':
##   method                  from      
##   +.gg_tsensemble         feasts    
##   autolayer.tbl_ts        fabletools
##   autoplot.dcmp_ts        fabletools
##   autoplot.tbl_ts         fabletools
##   grid.draw.gg_tsensemble feasts    
##   print.gg_tsensemble     feasts
## [[1]]

## 
## [[2]]

## 
## [[3]]

## 
## [[4]]

## 
## [[5]]

This time series has an overall increasing positive trend over time with some seasonality. There appears to be a slight increase in the earlier months of the year, from January until about June, and then a leveling out of employment. There is no evidence of any cyclic behavior; however there is are irregular dips in the employment in the early 90s and early 2000s.

# ?aus_production
ts_graphics(aus_production |> filter(year(Quarter) >= 1960), Bricks, 'Bricks (Million Units)', 'year')
## Warning: Removed 20 rows containing missing values (gg_lag).
## [[1]]
## Warning: Removed 20 rows containing missing values or values outside the scale range
## (`geom_line()`).

## 
## [[2]]
## Warning: Removed 20 rows containing missing values or values outside the scale range
## (`geom_line()`).

## 
## [[3]]
## Warning: Removed 5 rows containing missing values or values outside the scale range
## (`geom_line()`).

## 
## [[4]]

## 
## [[5]]

While this quarterly time series of brick production in Australia had an increasing trend until around the mid-70s, it lacks on overall increasing/decreasing trend. The lag plot also shows this by displaying a positive relationship decreases as the lags increase.There is a strong seasonal pattern with production increasing throughout quarters 2 and 3 and declining in quarters 4 and 1 each. year. This can be seen by looking at the seasonal plot and the seasonal subplots mean by quarter. This is further supported by the correlogram displaying peaks about every 4 quarters. Lastly, there does appear to be cyclicity with a pattern of sharp declines about every 5 years starting in the mid-70s.

# ?pelt
pelt |> autoplot(Hare)

pelt |> gg_subseries(Hare)

pelt |> gg_lag(Hare, geom = "point")
## Warning: `gg_lag()` was deprecated in feasts 0.4.2.
## ℹ Please use `ggtime::gg_lag()` instead.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.

pelt |>
    ACF(Hare) |>
    autoplot()

This time series shows a seasonal trend of around 10 years with a rapid increase in trading for 5 years followed buy a steep decline for 5 years. The ACF plot displays this seasonal pattern by having high autocorrelations in r~1 and r~10, as well as troughs in r~5 and r~15. The variance within this seasonal pattern is declining over time as seen by the decreasing max of the spiked trade records every 10 years. The time series strays from this seasonal pattern in 1860 and 1900. In these years, pelt trading had a slight increase during a time in which the lowest trasing was expected. The series does not exhibit a clear overall increasing/decreasing trend over the years and does not present cycle patterns.

# ?PBS
pbs_h02 = PBS |>
  filter(ATC2 == 'H02') |>
  select(Concession, Type, Cost)

pbs_h02 |>
  autoplot(Cost) +
  facet_wrap(vars(Concession, Type), scales = "free")

pbs_h02 |> gg_season(Cost)

pbs_h02 |> gg_subseries(Cost)

pbs_h02 |>
    ACF(Cost) |>
    autoplot()

Concessional/Co-Payments

  • Cyclicity: No cyclic behavior
  • Seasonality: There is an annual seasonal pattern with cost of concessional co-payments rising in the beginning of the year (Jan-May), leveling out mid-year (May-Aug), and then slightly decreasing at the end of the year (Aug-Dec).
  • Trends: Overall increasing positive trend over time

General/Co-Payments

  • White noise

Safety net subsidies

  • Cyclicity: No cyclic behavior
  • Seasonality: The cost of safety net scripts gradually starts to increase in June and continues rising into January with a sharp decline to $0 in February
    • Concessional safety net scripts increase as a higher rate and are more prevalent than general safety net scripts. Thus, this annual seasonal pattern is easier to discern in the concessional script graphics
  • Trends:
    • Concessional - Cost increases over time
    • General - Does not exhibit a clear overall increasing/decreasing trend over

The concessional co-payments and general safety net payments appear to have opposite seasonal trends which aligns with the understanding that safety net subsidies are provided to individuals exceeding their co-payment threshold.

# ?us_gasoline
us_gas = us_gasoline
us_gas |> autoplot(Barrels)

us_gas |> gg_season(Barrels)

# us_gas |> gg_subseries(Barrels, period='week')

us_gas |> gg_lag(Barrels, geom = "point")

us_gas |>
    ACF(Barrels) |>
    autoplot()

There seems to be pretty much an upward trend; however there is slight decline for about 10 years starting in 2005. There does not appear to be any apparent patterns of cyclicity or seasonality which can been seen by the positive increasing trend in the lag plots and, the autocorrelations for small lags are large and positive because observations close in time are also nearby in value.