DATA 624 HW2
Anjal Hussan
March 2023
Week 2 HW Problems
Exercises 3.1, 3.2, 3.3, 3.4, 3.5, 3.7, 3.8 and 3.9 from the online Hyndman book
library("fma")
library("xts")
library("ggplot2")
library("forecast")
library("fpp3")
library('lubridate')
library('tsibble')
library('readr')
library('readxl')3.1
Consider the GDP information in global_economy. Plot the GDP per capita for each country over time. Which country has the highest GDP per capita? How has this changed over time?
global_economy %>% autoplot(GDP/Population,show.legend=FALSE)
mutate_global_economy = global_economy %>% mutate(GDP_per_capita = GDP/Population)
mutate_global_economy %>% filter(GDP_per_capita >100000) %>%
autoplot(GDP_per_capita) +
labs(title = "GDP per capita", y="US Dollars")
arrange(mutate_global_economy, desc(GDP_per_capita))## # A tsibble: 15,150 x 10 [1Y]
## # Key: Country [263]
## Country Code Year GDP Growth CPI Imports Exports Popul…¹ GDP_p…²
## <fct> <fct> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 Monaco MCO 2014 7.06e9 7.18 NA NA NA 38132 185153.
## 2 Monaco MCO 2008 6.48e9 0.732 NA NA NA 35853 180640.
## 3 Liechtenstein LIE 2014 6.66e9 NA NA NA NA 37127 179308.
## 4 Liechtenstein LIE 2013 6.39e9 NA NA NA NA 36834 173528.
## 5 Monaco MCO 2013 6.55e9 9.57 NA NA NA 37971 172589.
## 6 Monaco MCO 2016 6.47e9 3.21 NA NA NA 38499 168011.
## 7 Liechtenstein LIE 2015 6.27e9 NA NA NA NA 37403 167591.
## 8 Monaco MCO 2007 5.87e9 14.4 NA NA NA 35111 167125.
## 9 Liechtenstein LIE 2016 6.21e9 NA NA NA NA 37666 164993.
## 10 Monaco MCO 2015 6.26e9 4.94 NA NA NA 38307 163369.
## # … with 15,140 more rows, and abbreviated variable names ¹Population,
## # ²GDP_per_capita3.2
For each of the following series, make a graph of the data. If transforming seems appropriate, do so and describe the effect.
- United States GDP from global_economy.
- Slaughter of Victorian “Bulls, bullocks and steers” in aus_livestock.
- Victorian Electricity Demand from vic_elec.
- Gas production from aus_production.
United States GDP from global_economy.
global_economy %>% filter(Country== "United States") %>%
autoplot() +
labs(title= "United States GDP",
y = "USD")
Slaughter of Victorian “Bulls, bullocks and steers” in
aus_livestock.
aus_livestock %>% filter(Animal == "Bulls, bullocks and steers", State == "Victoria") %>%
autoplot() +
labs(title= "Bulls, bullocks and steers"
)
Victorian Electricity Demand from vic_elec.
head(vic_elec)## # A tsibble: 6 x 5 [30m] <Australia/Melbourne>
## Time Demand Temperature Date Holiday
## <dttm> <dbl> <dbl> <date> <lgl>
## 1 2012-01-01 00:00:00 4383. 21.4 2012-01-01 TRUE
## 2 2012-01-01 00:30:00 4263. 21.0 2012-01-01 TRUE
## 3 2012-01-01 01:00:00 4049. 20.7 2012-01-01 TRUE
## 4 2012-01-01 01:30:00 3878. 20.6 2012-01-01 TRUE
## 5 2012-01-01 02:00:00 4036. 20.4 2012-01-01 TRUE
## 6 2012-01-01 02:30:00 3866. 20.2 2012-01-01 TRUEautoplot(vic_elec) +
labs(title = "30 Min Electricity Demand")
Gas production from aus_production
head(aus_production)## # A tsibble: 6 x 7 [1Q]
## Quarter Beer Tobacco Bricks Cement Electricity Gas
## <qtr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 1956 Q1 284 5225 189 465 3923 5
## 2 1956 Q2 213 5178 204 532 4436 6
## 3 1956 Q3 227 5297 208 561 4806 7
## 4 1956 Q4 308 5681 197 570 4418 6
## 5 1957 Q1 262 5577 187 529 4339 5
## 6 1957 Q2 228 5651 214 604 4811 7autoplot(aus_production, Gas) +
labs(title = "Australian Gas Production")
### 3.3 Why is a Box-Cox transformation unhelpful for the canadian_gas
data?
head(canadian_gas)## # A tsibble: 6 x 2 [1M]
## Month Volume
## <mth> <dbl>
## 1 1960 Jan 1.43
## 2 1960 Feb 1.31
## 3 1960 Mar 1.40
## 4 1960 Apr 1.17
## 5 1960 May 1.12
## 6 1960 Jun 1.01head(canadian_gas)## # A tsibble: 6 x 2 [1M]
## Month Volume
## <mth> <dbl>
## 1 1960 Jan 1.43
## 2 1960 Feb 1.31
## 3 1960 Mar 1.40
## 4 1960 Apr 1.17
## 5 1960 May 1.12
## 6 1960 Jun 1.01non_box_cox
non_box_cox = autoplot(canadian_gas)
non_box_cox
3.5
For the following series, find an appropriate Box-Cox transformation in order to stabilise the variance. Tobacco from aus_production, Economy class passengers between Melbourne and Sydney from ansett, and Pedestrian counts at Southern Cross Station from pedestrian.
Tobacco from aus_production
head(aus_production)## # A tsibble: 6 x 7 [1Q]
## Quarter Beer Tobacco Bricks Cement Electricity Gas
## <qtr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 1956 Q1 284 5225 189 465 3923 5
## 2 1956 Q2 213 5178 204 532 4436 6
## 3 1956 Q3 227 5297 208 561 4806 7
## 4 1956 Q4 308 5681 197 570 4418 6
## 5 1957 Q1 262 5577 187 529 4339 5
## 6 1957 Q2 228 5651 214 604 4811 7autoplot(aus_production, (Tobacco)) +
labs(title = "Tobacco Production")
aus_tobacco = aus_production %>%
select(Quarter, Tobacco)
lambda <- aus_tobacco %>%
features(Tobacco, features = guerrero) %>%
pull(lambda_guerrero)
aus_tobacco %>%
autoplot(box_cox(Tobacco, lambda)) +
labs(y = "",
title = "Transformed Tobacco Production ",
round(lambda,2))
No substantive transformation resulting from the Box-Cox
transformation
Economy class passengers between Melbourne and Sydney from ansett
head(ansett)## # A tsibble: 6 x 4 [1W]
## # Key: Airports, Class [1]
## Week Airports Class Passengers
## <week> <chr> <chr> <dbl>
## 1 1989 W28 ADL-PER Business 193
## 2 1989 W29 ADL-PER Business 254
## 3 1989 W30 ADL-PER Business 185
## 4 1989 W31 ADL-PER Business 254
## 5 1989 W32 ADL-PER Business 191
## 6 1989 W33 ADL-PER Business 136eco_Mel_syd = ansett %>% filter(Airports == "MEL-SYD", Class == "Economy")
autoplot(eco_Mel_syd) +
labs(title = "Weekly Economy Class Passengers. Airport: Melbourne and Sydeny")
lmda = eco_Mel_syd %>%
features(Passengers, features = guerrero) %>%
pull(lambda_guerrero)
eco_Mel_syd %>% autoplot(box_cox(Passengers, lmda)) 
Pedestrian counts at Southern Cross Station from pedestrian.
head(pedestrian)## # A tsibble: 6 x 5 [1h] <Australia/Melbourne>
## # Key: Sensor [1]
## Sensor Date_Time Date Time Count
## <chr> <dttm> <date> <int> <int>
## 1 Birrarung Marr 2015-01-01 00:00:00 2015-01-01 0 1630
## 2 Birrarung Marr 2015-01-01 01:00:00 2015-01-01 1 826
## 3 Birrarung Marr 2015-01-01 02:00:00 2015-01-01 2 567
## 4 Birrarung Marr 2015-01-01 03:00:00 2015-01-01 3 264
## 5 Birrarung Marr 2015-01-01 04:00:00 2015-01-01 4 139
## 6 Birrarung Marr 2015-01-01 05:00:00 2015-01-01 5 77scs_pedestrian <- pedestrian %>%
filter(Sensor == "Southern Cross Station")autoplot(scs_pedestrian, Count) +
labs(y = "Pedestrian Count",
title = "Hourly Pedestrian counts @ Southern Cross Station")
lambda_scs <- scs_pedestrian %>%
features(Count, features = guerrero) %>%
pull(lambda_guerrero)
#plot
scs_pedestrian %>%
autoplot(box_cox(Count, lambda_scs)) +
labs(y = "Transformed Pedestrian Counts",
title = ("Hourly Pedestrian counts at Southern Cross Station"))
3.9
- Write about 3–5 sentences describing the results of the decomposition. Pay particular attention to the scales of the graphs in making your interpretation.
- The
trendplot has direct impact onvaluesubplot. Thevalueplot is increasting as we go right just like thetrendplot - The
season_yearplot does show a regular pattern - The
remainderplot does make some impact on thevaluesubplot which is notable for years around 1991-1992
- Is the recession of 1991/1992 visible in the estimated
components?
Yes, the recession is visible in the estimated components.