DATA624_Week#2

DATA 624 Predictive Analytics

Homework #1: Time Series Graphics & Exploration

In this homework assignment, we were given the task to complete exercies 2.1, 2.2, 2.3, 2.4, 2.5, and 2.8 from the Hyndman online FOrecasting book. In these exercises, we are able to explore time series data.

Housekeeping

library(fpp3)

## Registered S3 method overwritten by 'tsibble':
##   method               from 
##   as_tibble.grouped_df dplyr

## ── Attaching packages ──────────────────────────────────────────── fpp3 1.0.1 ──

## ✔ tibble      3.2.1     ✔ tsibble     1.1.6
## ✔ dplyr       1.1.4     ✔ tsibbledata 0.4.1
## ✔ tidyr       1.3.1     ✔ feasts      0.4.1
## ✔ lubridate   1.9.4     ✔ fable       0.4.1
## ✔ ggplot2     3.5.1

## ── 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()

Exercise #2.1

Exploring Bricks Time Series

?aus_production

## starting httpd help server ... done

Explanation: By using this command, I am able to open up the “help” documentation for ‘aus_productions’ which gives me details about data set which in return I see that it is ‘Quarterly production of selected commodities in Australia’ For this specific assignment and exercise, I need to explore ‘Bricks’ from this dataset which is given the description of ‘clay brick production in millions of bricks’

aus_production %>%
  select(Bricks)

## # A tsibble: 218 x 2 [1Q]
##    Bricks Quarter
##     <dbl>   <qtr>
##  1    189 1956 Q1
##  2    204 1956 Q2
##  3    208 1956 Q3
##  4    197 1956 Q4
##  5    187 1957 Q1
##  6    214 1957 Q2
##  7    227 1957 Q3
##  8    222 1957 Q4
##  9    199 1958 Q1
## 10    229 1958 Q2
## # ℹ 208 more rows

Explanation: I want to see how the data looks like and I see there is a ‘Quarter’ column, so the time interval is quarterly

aus_production %>%
  autoplot(Bricks)

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

Exploring Lynx Time Series

?pelt

Explanation: Pelt is a pelt trading record where the time series is annual and Lynx is the number of Canadian pelts traded

pelt %>%
  autoplot(Lynx)

Exploring Close Time Series

?gafa_stock

Explanation: Looking at this documentation I can see that it is for GAFA Stock Prices where the time interval for this is daily and the Close is the data for the closing price for the stock

gafa_stock %>%
  autoplot(Close)

Exploring Demand Time Series

?vic_elec

Explanation: Looking at this datasets documentation, I can see that it is for Half-hourly electricity demand for Victoria, Australia where the time interval is half-hourly or ever 30 minutes. The Demand time series if for the total electricity demand in MWh

vic_elec %>%
  autoplot(Demand) +
  labs(y = "Total Electricity Demand in MWh", title = "Electricity Demand in Victoria, Australia")

Exercise 2.2:

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

glimpse(gafa_stock)

## Rows: 5,032
## Columns: 8
## Key: Symbol [4]
## $ Symbol    <chr> "AAPL", "AAPL", "AAPL", "AAPL", "AAPL", "AAPL", "AAPL", "AAP…
## $ Date      <date> 2014-01-02, 2014-01-03, 2014-01-06, 2014-01-07, 2014-01-08,…
## $ Open      <dbl> 79.38286, 78.98000, 76.77857, 77.76000, 76.97285, 78.11429, …
## $ High      <dbl> 79.57571, 79.10000, 78.11429, 77.99429, 77.93714, 78.12286, …
## $ Low       <dbl> 78.86000, 77.20428, 76.22857, 76.84571, 76.95571, 76.47857, …
## $ Close     <dbl> 79.01857, 77.28286, 77.70428, 77.14857, 77.63715, 76.64571, …
## $ Adj_Close <dbl> 66.96433, 65.49342, 65.85053, 65.37959, 65.79363, 64.95345, …
## $ Volume    <dbl> 58671200, 98116900, 103152700, 79302300, 64632400, 69787200,…

Explanation: The key in this case is Symbol, so we need to group by the key to see for each of the four stocks and we don’t need to see the rest of the columns in this case, so we will only need to look at the Symbol, Date, and Close. To look for the peak closing price, we need to filter by the MAX

gafa_stock %>%
  group_by(Symbol) %>%
  filter(Close == max(Close)) %>%
  select(Symbol, Date, Close)

## # A tsibble: 4 x 3 [!]
## # Key:       Symbol [4]
## # Groups:    Symbol [4]
##   Symbol Date       Close
##   <chr>  <date>     <dbl>
## 1 AAPL   2018-10-03  232.
## 2 AMZN   2018-09-04 2040.
## 3 FB     2018-07-25  218.
## 4 GOOG   2018-07-26 1268.

Exercise 2.3:

I put the tute1.csv file in my github repo, so we can call it without having it stored locally

library(tidyverse)

## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
## ✔ forcats 1.0.0     ✔ readr   2.1.5
## ✔ purrr   1.0.2     ✔ stringr 1.5.1
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter()     masks stats::filter()
## ✖ tsibble::interval() masks lubridate::interval()
## ✖ dplyr::lag()        masks stats::lag()
## ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errors

url <- "https://raw.githubusercontent.com/silmaxk/DATA624_PredictiveAnalytics/refs/heads/main/Homework%231/tute1.csv"

tute <- read.csv(url)

head(tute)

##      Quarter  Sales AdBudget   GDP
## 1 1981-03-01 1020.2    659.2 251.8
## 2 1981-06-01  889.2    589.0 290.9
## 3 1981-09-01  795.0    512.5 290.8
## 4 1981-12-01 1003.9    614.1 292.4
## 5 1982-03-01 1057.7    647.2 279.1
## 6 1982-06-01  944.4    602.0 254.0

Now to convert the data into time series

mytimeseries <- tute |>
  mutate(Quarter = yearquarter(Quarter)) |>
  as_tsibble(index = Quarter)

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 dont include ’facet_grid()

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

#### There is no clear distinction between the three series

Exercise 2.4:

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

Install the USgas package.
Create a tsibble from us_total with year as the index and state as the key.
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).

library(USgas)

gas <- us_total %>%
  as_tsibble(index = year, key = state)

new_england <- c('Maine','Vermont','New Hampshire', 'Massachusetts', 'Connecticut', 'Rhode Island')

gas %>%
  filter(state %in% new_england) %>%
  autoplot(y) +
  labs(title = "Natural Gas Consumption", subtitle = "New England Area", x = "Year", y = "Consumption")

Exercise 2.5:

Download tourism.xlsx from the book website and read it into R using readxl::read_excel().

library(readxl)

tourism <- read_excel('./tourism.xlsx')
head(tourism)

## # A tibble: 6 × 5
##   Quarter    Region   State           Purpose  Trips
##   <chr>      <chr>    <chr>           <chr>    <dbl>
## 1 1998-01-01 Adelaide South Australia Business  135.
## 2 1998-04-01 Adelaide South Australia Business  110.
## 3 1998-07-01 Adelaide South Australia Business  166.
## 4 1998-10-01 Adelaide South Australia Business  127.
## 5 1999-01-01 Adelaide South Australia Business  137.
## 6 1999-04-01 Adelaide South Australia Business  200.

Create a tsibble which is identical to the tourism tsibble from the tsibble package.

tourism_ts <- tourism %>%
  mutate(Quarter = yearquarter(Quarter)) %>%
  as_tsibble(index = Quarter, key = c('Region', 'Purpose', 'State'))

head(tourism_ts)

## # A tsibble: 6 x 5 [1Q]
## # Key:       Region, State, Purpose [1]
##   Quarter Region   State           Purpose  Trips
##     <qtr> <chr>    <chr>           <chr>    <dbl>
## 1 1998 Q1 Adelaide South Australia Business  135.
## 2 1998 Q2 Adelaide South Australia Business  110.
## 3 1998 Q3 Adelaide South Australia Business  166.
## 4 1998 Q4 Adelaide South Australia Business  127.
## 5 1999 Q1 Adelaide South Australia Business  137.
## 6 1999 Q2 Adelaide South Australia Business  200.

Find what combination of Region and Purpose had the maximum number of overnight trips on average.

tourism_ts %>%
  mutate(avg_trips = mean(Trips, na.rm = TRUE), .by = c(Region, Purpose), .keep = "none") %>%
  distinct() %>%
  arrange(desc(avg_trips)) %>%
  slice(1)

## # A tibble: 1 × 3
##   Region Purpose  avg_trips
##   <chr>  <chr>        <dbl>
## 1 Sydney Visiting      747.

Explanation: I needed some assistance with this portion and learned that:
mutate(avg_trips = mean(Trips, na.rm = TRUE), .by = c(Region, Purpose)) computes the average trips per combination of Region and Purpose
distinct() makes sure that all the unique combinations are still there
arrange(desc(avg_trips)) sorts the results in descending order
slice(1) picks the combination with the highest average from the rest so we get the result with the maximum number
Create a new tsibble which combines the Purposes and Regions, and just has total trips by State

total_trips_by_state <- tourism_ts %>%
  group_by(State = Region) %>%
  summarise(total_trips = sum(Trips, na.rm = TRUE))

head(total_trips_by_state)

## # A tsibble: 6 x 3 [1Q]
## # Key:       State [1]
##   State    Quarter total_trips
##   <chr>      <qtr>       <dbl>
## 1 Adelaide 1998 Q1        659.
## 2 Adelaide 1998 Q2        450.
## 3 Adelaide 1998 Q3        593.
## 4 Adelaide 1998 Q4        524.
## 5 Adelaide 1999 Q1        548.
## 6 Adelaide 1999 Q2        569.

Exercise 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 series?
What can you say about the seasonal patterns?
Can you identify any unusual years?

us_employment %>%
  filter(Title == "Total Private") %>%
  autoplot(Employed)

The graph for employment data shows a gradual increase in trend as the years go by and shows a dip around the year of around 2008-2010

aus_production %>%
  gg_season(Bricks)

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

The trend for the Bricks data was showing increase from around 1985-1995, but then since then the trend line has been decreasing over time. The lowest quarter for production would be the first quarter and since then has been increasing

pelt %>%
  gg_subseries(Hare)

The seasonality of this data is annual and the data shows a strong cyclic pattern with peaks and drops over time and it happens about ever 9-10 years. The highest peak happened around 1860s where the populations increased to over 150,000

us_gasoline %>%
  gg_lag(Barrels)

the lag plots helps us identify autocorrelation and with these results, there seems to be a strong diagonal pattern which indicates a strong positive correlation. Since there are no surprise colors coming through, it shows that there might be a consistent behavior over time

PBS %>%
  filter(ATC2 == "H02") %>%
  ACF(Cost) %>%
  autoplot()

This graph is divided into four panels which shows a different combination between payment types and categories. Most bars show a positive trend which shows that high costs are followed by more high costs. The blue dashed lined shows the 95% confidence intervals. In this case, the bars fall outside o the lines which means that autocorrelation is unlikely in this case

DATA624_Week#2_HW#1

Silma

2025-02-02

DATA 624 Predictive Analytics

Homework #1: Time Series Graphics & Exploration

In this homework assignment, we were given the task to complete exercies 2.1, 2.2, 2.3, 2.4, 2.5, and 2.8 from the Hyndman online FOrecasting book. In these exercises, we are able to explore time series data.

Housekeeping

Exercise #2.1

Exploring Bricks Time Series

Exploring Lynx Time Series

Exploring Close Time Series

Exploring Demand Time Series

Exercise 2.2:

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

Exercise 2.3:

I put the tute1.csv file in my github repo, so we can call it without having it stored locally

Now to convert the data into time series

Construct time series plots of each of the three series

Check what happens when you dont include ’facet_grid()

Exercise 2.4:

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

Exercise 2.5:

Exercise 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

The graph for employment data shows a gradual increase in trend as the years go by and shows a dip around the year of around 2008-2010

The trend for the Bricks data was showing increase from around 1985-1995, but then since then the trend line has been decreasing over time. The lowest quarter for production would be the first quarter and since then has been increasing

The seasonality of this data is annual and the data shows a strong cyclic pattern with peaks and drops over time and it happens about ever 9-10 years. The highest peak happened around 1860s where the populations increased to over 150,000

the lag plots helps us identify autocorrelation and with these results, there seems to be a strong diagonal pattern which indicates a strong positive correlation. Since there are no surprise colors coming through, it shows that there might be a consistent behavior over time