Data 624 - HW1
Habib Khan
September 6, 2020
library(fpp)
library(fpp2)
library(ggplot2)
library(kableExtra)Question 2.1
Use the help function to explore what the series gold, woolyrnq and gas represent.
- Use autoplot() to plot each of these in seperate plots.
- What is the frequency of each series? Hint: apply the frequency() function.
- Use which.max() to spot the outlier in the gold series. Which observation was it?
(a) Autoplot
autoplot(gold) + labs(title="Price History of Gold", x="Days",y="Dollar Price")
autoplot(woolyrnq) + labs(title="Price History of Woolen",y="Tons")
autoplot(gas) + labs(title="Gas Production")
(b) Frequency
print(paste0("Frequency for gold is ",frequency(gold)))## [1] "Frequency for gold is 1"print(paste0("Frequency for Woolen is ", frequency(woolyrnq)))## [1] "Frequency for Woolen is 4"print(paste0("Frequency for Gas is ", frequency(gas)))## [1] "Frequency for Gas is 12"(c) Outlier(s)
print(paste0("The observation number ", which.max(gold), " is an outlier"))## [1] "The observation number 770 is an outlier"Question 2.2
Download the file tute1.csv from 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.
(a) You can read the data into R by following script:
tute1 <- read.csv("https://otexts.com/fpp2/extrafiles/tute1.csv", header=TRUE)(b) Convert the data into timeseries object using ts()
mytimeseries <- ts(tute1[,-1], start=1981, frequency=4) # [,-1] removes date columns as ts() will convert into timeseries anyway(c) Construct time series plots of each of the three series
autoplot(mytimeseries,facets=TRUE)
## Check what happens when you don’t include facets=TRUE
autoplot(mytimeseries)
Question 2.3
Download some monthly Australian retail data from the book website. These represent retail sales in various categories for different Australian states, and are stored in a MS-Excel file.
(a) Read the data
retail <- readxl::read_excel("retail.xlsx", skip = 1) # Skipping the first row which had irrelevant information
retail %>% head() %>% kable() %>% kable_styling()| Series ID | A3349335T | A3349627V | A3349338X | A3349398A | A3349468W | A3349336V | A3349337W | A3349397X | A3349399C | A3349874C | A3349871W | A3349790V | A3349556W | A3349791W | A3349401C | A3349873A | A3349872X | A3349709X | A3349792X | A3349789K | A3349555V | A3349565X | A3349414R | A3349799R | A3349642T | A3349413L | A3349564W | A3349416V | A3349643V | A3349483V | A3349722T | A3349727C | A3349641R | A3349639C | A3349415T | A3349349F | A3349563V | A3349350R | A3349640L | A3349566A | A3349417W | A3349352V | A3349882C | A3349561R | A3349883F | A3349721R | A3349478A | A3349637X | A3349479C | A3349797K | A3349477X | A3349719C | A3349884J | A3349562T | A3349348C | A3349480L | A3349476W | A3349881A | A3349410F | A3349481R | A3349718A | A3349411J | A3349638A | A3349654A | A3349499L | A3349902A | A3349432V | A3349656F | A3349361W | A3349501L | A3349503T | A3349360V | A3349903C | A3349905J | A3349658K | A3349575C | A3349428C | A3349500K | A3349577J | A3349433W | A3349576F | A3349574A | A3349816F | A3349815C | A3349744F | A3349823C | A3349508C | A3349742A | A3349661X | A3349660W | A3349909T | A3349824F | A3349507A | A3349580W | A3349825J | A3349434X | A3349822A | A3349821X | A3349581X | A3349908R | A3349743C | A3349910A | A3349435A | A3349365F | A3349746K | A3349370X | A3349754K | A3349670A | A3349764R | A3349916R | A3349589T | A3349590A | A3349765T | A3349371A | A3349588R | A3349763L | A3349372C | A3349442X | A3349591C | A3349671C | A3349669T | A3349521W | A3349443A | A3349835L | A3349520V | A3349841J | A3349925T | A3349450X | A3349679W | A3349527K | A3349526J | A3349598V | A3349766V | A3349600V | A3349680F | A3349378T | A3349767W | A3349451A | A3349924R | A3349843L | A3349844R | A3349376L | A3349599W | A3349377R | A3349779F | A3349379V | A3349842K | A3349532C | A3349931L | A3349605F | A3349688X | A3349456L | A3349774V | A3349848X | A3349457R | A3349851L | A3349604C | A3349608L | A3349609R | A3349773T | A3349852R | A3349775W | A3349776X | A3349607K | A3349849A | A3349850K | A3349606J | A3349932R | A3349862V | A3349462J | A3349463K | A3349334R | A3349863W | A3349781T | A3349861T | A3349626T | A3349617R | A3349546T | A3349787F | A3349333L | A3349860R | A3349464L | A3349389X | A3349461F | A3349788J | A3349547V | A3349388W | A3349870V | A3349396W |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1982-04-01 | 303.1 | 41.7 | 63.9 | 408.7 | 65.8 | 91.8 | 53.6 | 211.3 | 94.0 | 32.7 | 126.7 | 178.3 | 50.4 | 22.2 | 43.0 | 62.4 | 178.0 | 61.8 | 85.4 | 147.2 | 1250.2 | 257.9 | 17.3 | 34.9 | 310.2 | 58.2 | 55.8 | 59.1 | 173.1 | 93.6 | 26.3 | 119.9 | 104.2 | 42.2 | 15.6 | 31.6 | 34.4 | 123.7 | 36.4 | 48.7 | 85.1 | 916.2 | 139.3 | NA | NA | 161.8 | 31.8 | 46.6 | 13.3 | 91.6 | 28.9 | 13.9 | 42.8 | 67.5 | 18.4 | 11.1 | 22.0 | 25.8 | 77.3 | 18.7 | 26.7 | 45.4 | 486.3 | 83.5 | 6.0 | 11.3 | 100.8 | 15.2 | 16.0 | 8.6 | 39.7 | 19.1 | 6.6 | 25.7 | 48.9 | 8.1 | 6.1 | 7.2 | 12.9 | 34.2 | 14.3 | 15.8 | 30.1 | 279.4 | 96.6 | 12.3 | 13.1 | 122.0 | 19.2 | 22.5 | 8.6 | 50.4 | 21.4 | 7.4 | 28.8 | 36.5 | 9.7 | 6.5 | 14.6 | 11.3 | 42.1 | 8.0 | 10.4 | 18.4 | 298.3 | 26.0 | NA | NA | 28.4 | 6.1 | 5.1 | 2.4 | 13.6 | 6.7 | 1.9 | 8.7 | NA | 2.9 | 1.8 | 4.0 | NA | NA | 1.9 | 3.5 | 5.4 | 79.9 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | 12.7 | 1.2 | 1.6 | 15.5 | 2.7 | 4.4 | 2.6 | 9.7 | 3.7 | 2.2 | 5.9 | 10.3 | 2.3 | 1.1 | 2.5 | 2.2 | 8.1 | 4.4 | 3.2 | 7.6 | 57.1 | 933.4 | 79.6 | 149.6 | 1162.6 | 200.3 | 243.4 | 148.6 | 592.3 | 268.5 | 91.4 | 359.9 | 460.1 | 135.1 | 64.9 | 125.6 | 153.5 | 479.1 | 146.3 | 196.1 | 342.4 | 3396.4 |
| 1982-05-01 | 297.8 | 43.1 | 64.0 | 404.9 | 65.8 | 102.6 | 55.4 | 223.8 | 105.7 | 35.6 | 141.3 | 202.8 | 49.9 | 23.1 | 45.3 | 63.1 | 181.5 | 60.8 | 84.8 | 145.6 | 1300.0 | 257.4 | 18.1 | 34.6 | 310.1 | 62.0 | 58.4 | 59.2 | 179.5 | 95.3 | 27.1 | 122.5 | 110.2 | 42.1 | 15.8 | 31.5 | 34.4 | 123.9 | 36.2 | 48.9 | 85.1 | 931.2 | 136.0 | NA | NA | 158.7 | 32.8 | 49.6 | 12.7 | 95.0 | 30.6 | 14.7 | 45.3 | 69.7 | 17.7 | 11.7 | 21.9 | 25.9 | 77.2 | 19.5 | 27.3 | 46.8 | 492.8 | 80.6 | 5.4 | 11.1 | 97.1 | 17.2 | 19.0 | 9.5 | 45.7 | 21.6 | 7.0 | 28.6 | 52.2 | 7.5 | 6.5 | 7.5 | 13.0 | 34.4 | 14.2 | 15.8 | 30.0 | 288.0 | 96.4 | 11.8 | 13.4 | 121.6 | 21.9 | 27.8 | 8.2 | 57.9 | 24.1 | 8.0 | 32.1 | 43.7 | 11.0 | 7.2 | 15.2 | 11.6 | 45.0 | 8.0 | 10.3 | 18.3 | 318.5 | 25.4 | NA | NA | 27.7 | 6.3 | 4.7 | 2.5 | 13.4 | 7.4 | 1.9 | 9.3 | NA | 2.9 | 1.9 | 4.0 | NA | NA | 2.0 | 3.5 | 5.5 | 78.9 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | 12.1 | 1.4 | 1.6 | 15.1 | 3.0 | 4.9 | 3.3 | 11.1 | 3.8 | 2.1 | 5.9 | 10.6 | 2.5 | 1.0 | 2.5 | 2.0 | 8.0 | 3.4 | 3.3 | 6.7 | 57.3 | 920.5 | 80.8 | 149.7 | 1150.9 | 210.3 | 268.3 | 151.0 | 629.6 | 289.8 | 96.8 | 386.6 | 502.6 | 134.9 | 67.7 | 128.7 | 154.8 | 486.1 | 145.5 | 196.6 | 342.1 | 3497.9 |
| 1982-06-01 | 298.0 | 40.3 | 62.7 | 401.0 | 62.3 | 105.0 | 48.4 | 215.7 | 95.1 | 32.5 | 127.6 | 176.3 | 48.0 | 22.8 | 43.7 | 59.6 | 174.1 | 58.7 | 80.7 | 139.4 | 1234.2 | 261.2 | 18.1 | 34.6 | 313.9 | 53.8 | 53.7 | 59.8 | 167.3 | 85.2 | 24.3 | 109.6 | 96.7 | 38.5 | 15.2 | 29.6 | 33.5 | 116.8 | 35.7 | 47.1 | 82.8 | 887.0 | 143.5 | NA | NA | 166.6 | 34.9 | 51.4 | 12.9 | 99.2 | 30.5 | 14.5 | 45.1 | 60.7 | 17.7 | 11.5 | 22.7 | 25.9 | 77.7 | 18.6 | 26.2 | 44.8 | 494.1 | 82.3 | 5.2 | 11.2 | 98.7 | 17.4 | 18.1 | 8.4 | 43.9 | 18.3 | 6.0 | 24.3 | 48.9 | 6.7 | 6.1 | 7.5 | 12.5 | 32.7 | 13.4 | 15.3 | 28.7 | 277.2 | 95.6 | 11.3 | 13.5 | 120.4 | 19.9 | 26.7 | 7.9 | 54.4 | 21.4 | 7.0 | 28.5 | 38.0 | 10.7 | 6.6 | 14.5 | 10.9 | 42.5 | 7.3 | 10.4 | 17.7 | 301.5 | 25.3 | NA | NA | 27.7 | 6.4 | 5.2 | 2.1 | 13.7 | 6.7 | 1.8 | 8.6 | NA | 2.9 | 1.9 | 3.9 | NA | NA | 2.0 | 3.1 | 5.1 | 77.5 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | 12.5 | 1.3 | 1.7 | 15.5 | 2.5 | 4.8 | 2.7 | 9.9 | 3.2 | 2.0 | 5.1 | 9.9 | 2.3 | 1.0 | 2.5 | 2.0 | 7.8 | 3.6 | 3.5 | 7.1 | 55.3 | 933.6 | 77.3 | 149.0 | 1160.0 | 198.7 | 266.1 | 142.6 | 607.4 | 261.9 | 88.6 | 350.5 | 443.8 | 128.2 | 65.5 | 125.0 | 148.8 | 467.5 | 140.2 | 188.5 | 328.7 | 3357.8 |
| 1982-07-01 | 307.9 | 40.9 | 65.6 | 414.4 | 68.2 | 106.0 | 52.1 | 226.3 | 95.3 | 33.5 | 128.8 | 172.6 | 48.6 | 23.2 | 46.5 | 61.9 | 180.2 | 60.3 | 82.4 | 142.7 | 1265.0 | 266.1 | 18.9 | 35.2 | 320.2 | 57.9 | 56.9 | 59.8 | 174.5 | 91.6 | 25.6 | 117.2 | 104.6 | 38.9 | 15.2 | 35.2 | 33.4 | 122.7 | 34.6 | 47.5 | 82.1 | 921.3 | 150.2 | NA | NA | 172.9 | 34.6 | 50.9 | 13.9 | 99.4 | 27.9 | 15.2 | 43.1 | 67.9 | 18.4 | 13.1 | 24.3 | 28.7 | 84.4 | 22.6 | 25.2 | 47.8 | 515.6 | 88.2 | 5.6 | 12.1 | 105.9 | 18.7 | 20.3 | 10.3 | 49.3 | 18.6 | 6.4 | 25.0 | 48.3 | 7.8 | 6.6 | 7.9 | 13.9 | 36.2 | 14.5 | 17.0 | 31.4 | 296.1 | 103.3 | 12.1 | 13.8 | 129.2 | 19.3 | 28.2 | 8.7 | 56.2 | 21.8 | 7.2 | 29.0 | 42.0 | 9.0 | 7.0 | 14.6 | 11.4 | 42.0 | 7.8 | 10.3 | 18.1 | 316.4 | 27.8 | NA | NA | 30.3 | 5.9 | 5.2 | 2.7 | 13.7 | 7.1 | 1.8 | 8.9 | NA | 3.1 | 1.8 | 4.4 | NA | NA | 1.9 | 3.6 | 5.5 | 82.7 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | 13.2 | 1.4 | 1.6 | 16.1 | 2.8 | 5.1 | 2.4 | 10.2 | 3.4 | 2.1 | 5.4 | 8.8 | 2.6 | 1.1 | 2.6 | 2.0 | 8.3 | 4.0 | 3.5 | 7.5 | 56.3 | 972.6 | 80.4 | 153.5 | 1206.4 | 208.7 | 273.5 | 150.1 | 632.4 | 267.2 | 92.1 | 359.3 | 459.1 | 129.9 | 68.5 | 136.6 | 156.1 | 491.1 | 146.5 | 192.0 | 338.5 | 3486.8 |
| 1982-08-01 | 299.2 | 42.1 | 62.6 | 403.8 | 66.0 | 96.9 | 54.2 | 217.1 | 82.8 | 29.4 | 112.3 | 169.6 | 51.3 | 21.4 | 44.8 | 60.7 | 178.1 | 56.1 | 80.7 | 136.8 | 1217.6 | 247.2 | 19.0 | 33.8 | 300.1 | 59.2 | 56.7 | 62.2 | 178.1 | 85.2 | 23.5 | 108.7 | 92.5 | 39.5 | 14.5 | 34.7 | 33.2 | 122.0 | 32.5 | 49.3 | 81.8 | 883.2 | 144.0 | NA | NA | 165.9 | 32.9 | 51.6 | 12.8 | 97.3 | 27.4 | 14.1 | 41.5 | 66.5 | 17.8 | 13.0 | 23.6 | 27.7 | 82.1 | 22.6 | 25.6 | 48.2 | 501.4 | 82.3 | 5.7 | 11.7 | 99.7 | 18.6 | 19.6 | 10.6 | 48.9 | 17.1 | 6.0 | 23.1 | 49.4 | 7.9 | 6.3 | 8.3 | 13.7 | 36.1 | 13.6 | 17.5 | 31.1 | 288.4 | 96.6 | 12.0 | 13.3 | 121.9 | 19.6 | 27.4 | 7.9 | 55.0 | 18.7 | 6.6 | 25.3 | 38.5 | 9.1 | 6.8 | 15.3 | 10.9 | 42.1 | 7.6 | 10.1 | 17.7 | 300.5 | 26.6 | NA | NA | 29.0 | 5.7 | 4.8 | 2.9 | 13.4 | 5.8 | 1.7 | 7.5 | NA | 3.1 | 1.8 | 4.2 | NA | NA | 1.9 | 3.6 | 5.5 | 78.1 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | 12.7 | 1.6 | 1.6 | 15.8 | 2.8 | 4.6 | 2.7 | 10.1 | 3.1 | 2.0 | 5.0 | 8.8 | 2.6 | 0.9 | 2.8 | 2.0 | 8.4 | 3.6 | 3.7 | 7.3 | 55.4 | 923.5 | 81.6 | 147.3 | 1152.5 | 206.2 | 262.7 | 153.7 | 622.6 | 241.5 | 83.7 | 325.2 | 438.4 | 133.0 | 65.2 | 134.7 | 152.8 | 485.7 | 138.8 | 192.7 | 331.5 | 3355.9 |
| 1982-09-01 | 305.4 | 42.0 | 64.4 | 411.8 | 62.3 | 97.5 | 53.6 | 213.4 | 89.4 | 32.2 | 121.6 | 181.4 | 49.6 | 21.8 | 43.9 | 61.2 | 176.5 | 58.1 | 82.1 | 140.2 | 1244.9 | 262.4 | 18.4 | 35.4 | 316.2 | 57.1 | 58.9 | 63.6 | 179.6 | 89.5 | 24.3 | 113.8 | 98.3 | 41.7 | 15.1 | 34.2 | 34.5 | 125.5 | 33.9 | 50.7 | 84.6 | 917.9 | 146.9 | NA | NA | 169.5 | 33.7 | 49.6 | 14.5 | 97.9 | 29.1 | 15.5 | 44.5 | 73.4 | 18.8 | 13.0 | 21.8 | 29.0 | 82.6 | 23.2 | 26.7 | 49.8 | 517.7 | 84.2 | 5.8 | 12.0 | 102.0 | 18.8 | 19.9 | 11.5 | 50.2 | 18.2 | 6.4 | 24.6 | 48.5 | 7.8 | 6.4 | 7.8 | 14.1 | 36.0 | 13.9 | 17.8 | 31.7 | 293.0 | 101.4 | 12.3 | 13.4 | 127.1 | 19.9 | 27.0 | 8.7 | 55.6 | 19.5 | 7.4 | 26.9 | 40.2 | 10.0 | 7.1 | 15.1 | 11.7 | 43.9 | 8.2 | 10.3 | 18.5 | 312.3 | 27.1 | NA | NA | 29.6 | 5.3 | 4.8 | 2.6 | 12.8 | 5.8 | 1.7 | 7.5 | NA | 3.2 | 1.8 | 4.0 | NA | NA | 1.9 | 3.8 | 5.7 | 79.1 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | 12.9 | 1.4 | 1.8 | 16.0 | 2.6 | 4.3 | 3.1 | 10.0 | 3.4 | 2.2 | 5.6 | 9.2 | 2.6 | 1.0 | 2.8 | 2.2 | 8.6 | 4.2 | 3.9 | 8.1 | 57.5 | 955.9 | 81.4 | 151.8 | 1189.1 | 200.9 | 263.1 | 157.9 | 622.0 | 256.2 | 90.1 | 346.3 | 465.1 | 135.5 | 66.8 | 130.4 | 157.2 | 489.9 | 144.3 | 197.6 | 341.9 | 3454.3 |
(b) Select one of the time series as follows (but replace the column name with your own chosen column):
myts <- ts(retail[,"A3349336V"],
frequency=12, start=c(1982,4))
myts## Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
## 1982 91.8 102.6 105.0 106.0 96.9 97.5 99.3 107.8 155.5
## 1983 95.1 105.1 124.1 112.3 120.5 115.0 111.7 117.2 106.9 114.4 136.5 189.0
## 1984 95.4 105.8 107.5 90.4 110.0 102.6 111.0 105.2 93.9 103.3 117.2 170.4
## 1985 100.7 92.0 106.6 103.6 122.3 107.8 124.5 116.8 109.8 117.3 135.1 191.8
## 1986 114.0 103.2 106.8 102.9 121.2 109.2 133.7 127.5 123.5 117.9 124.6 188.0
## 1987 111.9 103.3 113.5 119.6 134.9 139.0 133.1 125.0 126.4 139.8 145.8 225.2
## 1988 130.6 136.4 151.7 140.9 163.4 150.0 146.5 149.0 141.0 133.8 161.1 225.3
## 1989 143.8 133.6 148.0 144.1 168.8 173.9 166.7 170.8 172.0 175.1 189.6 253.9
## 1990 171.6 158.9 175.5 165.7 190.2 173.1 173.9 181.1 171.4 189.2 194.9 280.2
## 1991 186.3 170.8 171.7 170.0 186.9 170.5 193.5 194.2 175.8 194.6 196.8 257.6
## 1992 191.7 184.8 185.1 181.7 189.4 189.5 206.2 183.0 189.9 198.6 201.4 293.3
## 1993 196.0 176.5 198.4 181.5 196.4 193.4 207.6 194.6 206.9 225.0 224.8 295.7
## 1994 202.7 182.9 207.6 189.6 214.8 208.2 216.5 243.5 206.5 226.1 253.5 356.5
## 1995 232.7 204.5 229.1 217.7 250.3 238.7 228.9 219.3 219.2 215.2 246.7 340.0
## 1996 238.0 227.5 253.3 235.9 262.3 262.6 262.2 251.6 238.0 244.8 249.8 351.5
## 1997 227.5 236.5 235.4 223.3 261.4 257.0 254.3 234.5 226.1 231.8 227.9 344.0
## 1998 243.0 213.7 244.7 231.2 242.7 243.4 240.8 223.3 212.7 216.2 210.8 325.7
## 1999 239.8 207.5 212.0 219.4 217.4 224.8 225.7 232.7 226.7 233.0 236.8 349.3
## 2000 217.3 221.5 225.1 205.4 250.8 301.9 230.6 246.7 236.1 254.4 271.1 388.0
## 2001 274.9 251.1 261.7 230.5 257.5 266.9 276.9 271.8 243.1 254.8 292.2 414.3
## 2002 289.7 234.5 253.3 264.1 312.6 310.7 292.7 296.6 274.2 295.2 322.4 447.3
## 2003 314.1 263.1 279.9 266.1 301.0 300.3 297.2 289.3 282.4 320.0 326.3 470.1
## 2004 345.1 291.5 312.7 286.8 306.1 331.7 346.8 325.7 320.2 356.7 381.9 528.4
## 2005 365.5 318.5 335.7 340.3 366.7 376.5 362.0 353.9 352.7 348.6 381.5 568.4
## 2006 384.6 311.0 340.1 321.0 364.8 399.1 374.5 357.9 362.7 383.1 417.8 618.5
## 2007 412.8 358.3 410.5 364.7 392.5 439.7 422.8 426.7 420.5 420.4 477.5 704.6
## 2008 472.2 403.9 410.8 437.9 445.4 493.4 455.4 451.8 433.9 459.7 484.7 782.7
## 2009 492.8 405.5 443.7 427.0 460.7 527.9 485.8 464.2 428.3 463.0 513.7 731.0
## 2010 491.9 392.7 428.7 432.6 465.4 516.3 476.5 472.5 437.8 461.8 490.4 720.9
## 2011 439.1 384.1 418.3 394.4 436.7 470.8 428.7 423.9 420.0 418.6 455.5 675.9
## 2012 407.8 343.0 391.9 364.1 415.5 453.1 434.6 419.9 412.2 412.6 459.0 673.9
## 2013 441.7 394.4 404.0 385.3 406.1 454.8 434.0 423.2 401.3 401.1 444.0 667.2(C) Explore your chosen retail time series using the following functions:
autoplot(), ggseasonplot(), ggsubseriesplot(), gglagplot(), ggAcf()
Can you spot any seasonality, cyclicity and trend? What do you learn about the series?
autoplot(myts) + labs(title="Turnover ; New South Wales ; Electrical and electronic goods retailing") # autoplot
ggseasonplot(myts) +labs(title="Turnover ; New South Wales ; Electrical and electronic goods retailing") # seasonplot
ggsubseriesplot(myts) + labs(title="Turnover ; New South Wales ; Electrical and electronic goods retailing") # ggsubseries plot
gglagplot(myts) + labs(title="Turnover ; New South Wales ; Electrical and electronic goods retailing") # lagplot
ggAcf(myts) + labs(title="Turnover ; New South Wales ; Electrical and electronic goods retailing")
Overall, the trend shows that turnover is increasing over the years with cyclical fluctuations in the long run. If you take a look at seasonal plot, overall it shows that trend is similar every year. The turnover drops in February and then slowly increases till June and then drops back till September and gradually increases by November and jumps very significantly through December. subseries plot shows that more or less turnover is kind of same from January through November but significantly high in December which shows similar trend in couple decades.
Question 2.6
Use the following graphics function: autoplot(), ggseasonplot(), ggsubseriesplot(), gglagplot(), ggACf() and explore features from the following time series: hsales, usdeaths, bricksq, sunspotarea and gasoline.
(a) Can you spot any seasonality, cyclical and trend?
hsales data
autoplot(hsales)
ggseasonplot(hsales)
ggsubseriesplot(hsales)
gglagplot(hsales)
ggAcf(hsales)
Over the 5 years, a cyclical trend has been seen in the above autoplot. Over the years, it keeps going up and down which shows its cyclical trend. In March and April, seaonality plot shows that the sales go up and the gradually reduces over few months throughout the year more and less.
usdeaths dataset
autoplot(usdeaths)
ggseasonplot(usdeaths)
ggsubseriesplot(usdeaths)
gglagplot(usdeaths)
ggAcf(usdeaths)
usdeaths has cyclical trend which keeps going up one year and goes next down next year. For instance, in 1973 it was very high and dipped all the way to almost 7000 from 11000 and then next year it went up at 10,000 and so and so forth. Seasonalplot shows that most of the deaths occur during summer which is the peak of deaths as compared with the other time of the year.
bricksq dataset
autoplot(bricksq)
ggseasonplot(bricksq)
ggsubseriesplot(bricksq)
gglagplot(bricksq)
ggAcf(bricksq)
Over the years, trend is increasing from 1960s through 1990s other than mid 83-84 where there was a significant drop in data. There is no seasonality in all quarters other slight difference in Q2 and Q3 which again is not huge gap.
sunspot area
autoplot(sunspotarea)
gglagplot(sunspotarea)
ggAcf(sunspotarea)
This data is not seasonal that’s why I did not plot ggseaonplot(). The data is cyclical and sunspotarea goes up and down in a cyclical manner throughout the time.
gasonline datasets
autoplot(gasoline)
ggseasonplot(gasoline)
gglagplot(gasoline)
ggAcf(gasoline)
Gasoline dataset has upward trend from 1990 and 2015 with slight dip from 2007 till 2013 but still it has been increasing. There is very little seasonality i.e. very slight rise during summer