Email         : juliansalomo2@gmail.com
RPubs       : https://rpubs.com/juliansalomo/
Department : Business Statistics
Address : ARA Center, Matana University Tower
   Jl. CBD Barat Kav, RT.1, Curug Sangereng, Kelapa Dua, Tangerang, Banten 15810.

1 Use the help function to explore what the series gafa_stock, PBS, vic_elec and peltrepresent.

1.1 GAFA stock prices

?gafa_stock
paste("gafa_stock is a time series of Historical stock prices from 2014-2018 for Google, Amazon, Facebook and Apple. ")

## [1] "gafa_stock is a time series of Historical stock prices from 2014-2018 for Google, Amazon, Facebook and Apple. "

datatable(gafa_stock,
          caption = htmltools::tags$caption(
            style = 'caption-side: bottom; text-align: center;',
            htmltools::em('Table GAFA stock prices.')),
            extensions = 'FixedColumns',
            option = list(scrollX = TRUE, fixedColumns = TRUE)
          )

Autoplot of gafa_stock

gafa_stock %>% autoplot(Close)

Time interval of gafa_stock

interval(gafa_stock)

## <interval[1]>
## [1] !

exclamation mark means there is no fix interval for gafa_stock

1.2 Monthly Medicare Australia prescription data

?PBS
paste("PBS is a monthly tsibble with two values:Scripts (Total number of scripts), Cost (Cost of the scripts in $AUD)")

## [1] "PBS is a monthly tsibble with two values:Scripts (Total number of scripts), Cost (Cost of the scripts in $AUD)"

head(PBS)

## # A tsibble: 6 x 9 [1M]
## # Key:       Concession, Type, ATC1, ATC2 [1]
##      Month Concession  Type   ATC1  ATC1_desc    ATC2  ATC2_desc   Scripts  Cost
##      <mth> <chr>       <chr>  <chr> <chr>        <chr> <chr>         <dbl> <dbl>
## 1 1991 Jul Concession~ Co-pa~ A     Alimentary ~ A01   STOMATOLOG~   18228 67877
## 2 1991 Aug Concession~ Co-pa~ A     Alimentary ~ A01   STOMATOLOG~   15327 57011
## 3 1991 Sep Concession~ Co-pa~ A     Alimentary ~ A01   STOMATOLOG~   14775 55020
## 4 1991 Oct Concession~ Co-pa~ A     Alimentary ~ A01   STOMATOLOG~   15380 57222
## 5 1991 Nov Concession~ Co-pa~ A     Alimentary ~ A01   STOMATOLOG~   14371 52120
## 6 1991 Dec Concession~ Co-pa~ A     Alimentary ~ A01   STOMATOLOG~   15028 54299

Autoplot of PBS

PBS %>% autoplot(Cost)

Time interval of PBS

interval(PBS)

## <interval[1]>
## [1] 1M

1M means the time interval of PBS is monthly

1.3 Half-hourly electricity demand for Victoria, Australia

?vic_elec
paste("vic_elec is a half-hourly tsibble with three values")

## [1] "vic_elec is a half-hourly tsibble with three values"

datatable(vic_elec,
          caption = htmltools::tags$caption(
            style = 'caption-side: bottom; text-align: center;',
            htmltools::em('Table Half-hourly electricity demand for Victoria, Australia.')),
            extensions = 'FixedColumns',
            option = list(scrollX = TRUE, fixedColumns = TRUE)
          )

Autoplot of vic_elec

vic_elec %>% autoplot(Demand)

Time interval of vic_elec

interval(vic_elec)

## <interval[1]>
## [1] 30m

30m means the time interval of vic_elec is half-hourly

1.4 Pelt trading records

?pelt
paste("Pelt is a time series of Hudson Bay Company trading records for Snowshoe Hare and Canadian Lynx furs from 1845 to 1935. This data contains trade records for all areas of the company.")

## [1] "Pelt is a time series of Hudson Bay Company trading records for Snowshoe Hare and Canadian Lynx furs from 1845 to 1935. This data contains trade records for all areas of the company."

datatable(pelt,
          caption = htmltools::tags$caption(
            style = 'caption-side: bottom; text-align: center;',
            htmltools::em('Table Pelt trading records.')),
            extensions = 'FixedColumns',
            option = list(scrollX = TRUE, fixedColumns = TRUE)
          )

Autoplot of pelt

pelt %>% autoplot(Lynx)

Time interval of pelt

interval(pelt)

## <interval[1]>
## [1] 1Y

1Y means the time interval of pelt is yearly

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

gafa_stock %>% group_by(Symbol) %>% filter(Close == max(Close))

## # A tsibble: 4 x 8 [!]
## # Key:       Symbol [4]
## # Groups:    Symbol [4]
##   Symbol Date        Open  High   Low Close Adj_Close   Volume
##   <chr>  <date>     <dbl> <dbl> <dbl> <dbl>     <dbl>    <dbl>
## 1 AAPL   2018-10-03  230.  233.  230.  232.      230. 28654800
## 2 AMZN   2018-09-04 2026. 2050. 2013  2040.     2040.  5721100
## 3 FB     2018-07-25  216.  219.  214.  218.      218. 58954200
## 4 GOOG   2018-07-26 1251  1270. 1249. 1268.     1268.  2405600

3 Download the file tute1.csv, 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.

3.1 You can read the data into R with the following script:

tute1 <- readr::read_csv("tute1.csv")
datatable(tute1,
          caption = htmltools::tags$caption(
            style = 'caption-side: bottom; text-align: center;',
            htmltools::em('Quarterly sales for a small company over the period 1981-2005')),
            extensions = 'FixedColumns',
            option = list(scrollX = TRUE, fixedColumns = TRUE)
          )

3.2 Convert the data to time series

mytimeseries <- tute1 %>%
  mutate(Quarter = yearmonth(Quarter)) %>%
  as_tsibble(index = Quarter)

3.3 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 we don’t include facet_grid(), all of the plot will not be divided and will be placed in one graph. Also there will be no name tag for each plot which means we can only read it from the color only.

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

4.1 Install the `USgas` package.

#install.packages("USgas")
library(USgas)

4.2 Create a tsibble from us_total with year as the index and state as the key.

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

4.3 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).

new_england<- us_total %>% 
              group_by(state) %>% 
              filter(state %in% c('Maine', 'Vermont', 'New 
                                  Hampshire', 'Massachusetts', 
                                  'Connecticut' ,'Rhode Island')) %>%
              ungroup()
new_england %>% autoplot(y)

5 Follow the instructions below:

5.1 Download `tourism.xlsx` here and read it into R using `readxl::read_excel()`.

tourism <-read_excel("tourism.xlsx")
datatable(tourism,
          caption = htmltools::tags$caption(
            style = 'caption-side: bottom; text-align: center;',
            htmltools::em('Tourism')),
            extensions = 'FixedColumns',
            option = list(scrollX = TRUE, fixedColumns = TRUE)
          )

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

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

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

tourism_tsibble %>% group_by(Region, Purpose) %>%
                    summarise(Trips = mean(Trips)) %>%
                    ungroup() %>%
                    filter(Trips == max(Trips))

## # A tsibble: 1 x 4 [1Q]
## # Key:       Region, Purpose [1]
##   Region    Purpose  Quarter Trips
##   <chr>     <chr>      <qtr> <dbl>
## 1 Melbourne Visiting 2017 Q4  985.

5.4 Create a new tsibble which combines the Purposes and Regions, and just has total trips by State.

tourism_tsibble %>% 
                    group_by(State) %>% 
                    summarise(Trips = sum(Trips)) %>%
                    ungroup()

## # 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

6 Create time plots of the following four time series: Bricks from aus_production, Lynx from pelt, Close from gafa_stock, Demand from vic_elec.

aus_production

aus_production %>% autoplot(Bricks)

pelt

pelt %>% autoplot(Lynx)

gafastock

gafa_stock %>% autoplot(Close)

vic_elec

vic_elec %>% autoplot(Demand)

6.1 Use ? (or help()) to find out about the data in each series.

6.2 For the last plot, modify the axis labels and title.(Demand from vic_elec)

vic_elec %>% ggplot(aes(x= Date, y= Demand, group = Holiday)) +
 geom_line(aes(col=Holiday)) +
 facet_grid(Holiday ~ ., scales ="free" )

7 The aus_arrivals data set comprises quarterly international arrivals to Australia from Japan, New Zealand, UK and the US.

datatable(aus_arrivals,
          caption = htmltools::tags$caption(
            style = 'caption-side: bottom; text-align: center;',
            htmltools::em('data set comprises quarterly international arrivals to Australia from Japan, New Zealand, UK and the US')),
            extensions = 'FixedColumns',
            option = list(scrollX = TRUE, fixedColumns = TRUE)
          )

7.1 Use autoplot(), gg_season() and gg_subseries() to compare the differences between the arrivals from these four countries.

aus_arrivals %>% autoplot(Arrivals)

aus_arrivals %>% gg_season(Arrivals)

aus_arrivals %>% gg_subseries(Arrivals)

7.2 Can you identify any unusual observations?

The arrivals from Japan decrease a lot in 2nd quarter compared to the other quarteres.
The arrivals from New Zealand are highest in 3rd quarter and lowest in 1st quarter.
The arrivals from UK and US are low in 2nd and 3rd quarters and high in 1st and 4th quarters.

8 Monthly Australian retail data is provided in aus_retail. Select one of the time series as follows (but choose your own seed value):

Explore your chosen retail time series using the following functions:

set.seed(12345678)
myseries <- aus_retail %>%
  filter(`Series ID` == sample(aus_retail$`Series ID`,1))

Explore your chosen retail time series using the following functions:

autoplot(), gg_season(), gg_subseries(), gg_lag(), ACF() %>% autoplot()

Can you spot any seasonality, cyclicity and trend? What do you learn about the series?

myseries %>% autoplot(Turnover)

myseries %>% gg_season(Turnover)

myseries %>% gg_subseries(Turnover)

myseries %>% gg_lag(Turnover)

myseries %>% ACF(Turnover) %>%
 autoplot()

* From the autoplot, we can see a clear seasonal or cyclic pattern in the time series, and a upward trend.

The seasonal plot shows that there are indeed seasonal patterns. The plot also reveals that there is a typical big jump every year in December, and a drop in February. Sales begin to increase in the fall, peaking between November and December, then decreasing after January, likely to coincide with holiday shopping and sales for Christmas.
The seasonal subseries offers a new perspective on seasonality by showing the monthly mean values. We see a large increase from November to December and a decrease from December to February, but also a small, decreasing trend in turnover from January to June and a similar increase from July to November, before the big spike from November to December.

*In this lag graph, the data is difficult to analyze. We can see some negative and positive relationships, but due to the high number of graphs and the fact that this is a monthly graph, it’s hard to tell much different.

The ACF shows powerful, statistically significant autocorrelation, showing that the lagged values get a linear relationship. The small drop in the amount of the ACF over time supports a pattern, as does seasonality with spikes at 12 and 24, the December increase.

9 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 us_gasoline.

“Total Private” Employed from us_employment

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

Priv %>% gg_season(Employed)

Priv %>% gg_subseries(Employed)

Priv %>% gg_lag(Employed)

Priv %>% ACF(Employed)

## # A tsibble: 29 x 3 [1M]
## # Key:       Series_ID [1]
##    Series_ID       lag   acf
##    <chr>         <lag> <dbl>
##  1 CEU0500000001    1M 0.997
##  2 CEU0500000001    2M 0.993
##  3 CEU0500000001    3M 0.990
##  4 CEU0500000001    4M 0.986
##  5 CEU0500000001    5M 0.983
##  6 CEU0500000001    6M 0.980
##  7 CEU0500000001    7M 0.977
##  8 CEU0500000001    8M 0.974
##  9 CEU0500000001    9M 0.971
## 10 CEU0500000001   10M 0.968
## # ... with 19 more rows

Bricks from aus_production

aus_production %>% autoplot(Bricks)

aus_production %>% gg_season(Bricks)

aus_production %>% gg_subseries(Bricks)

aus_production %>% gg_lag(Bricks)

aus_production %>% ACF(Bricks)

## # A tsibble: 22 x 2 [1Q]
##      lag   acf
##    <lag> <dbl>
##  1    1Q 0.900
##  2    2Q 0.815
##  3    3Q 0.813
##  4    4Q 0.828
##  5    5Q 0.720
##  6    6Q 0.642
##  7    7Q 0.655
##  8    8Q 0.692
##  9    9Q 0.609
## 10   10Q 0.556
## # ... with 12 more rows

Hare from pelt

pelt %>% autoplot(Hare)

pelt %>% gg_subseries(Hare)

pelt %>% gg_lag(Hare)

pelt %>% ACF(Hare)

## # A tsibble: 19 x 2 [1Y]
##      lag     acf
##    <lag>   <dbl>
##  1    1Y  0.658 
##  2    2Y  0.214 
##  3    3Y -0.155 
##  4    4Y -0.401 
##  5    5Y -0.493 
##  6    6Y -0.401 
##  7    7Y -0.168 
##  8    8Y  0.113 
##  9    9Y  0.307 
## 10   10Y  0.340 
## 11   11Y  0.296 
## 12   12Y  0.206 
## 13   13Y  0.0372
## 14   14Y -0.153 
## 15   15Y -0.285 
## 16   16Y -0.295 
## 17   17Y -0.202 
## 18   18Y -0.0676
## 19   19Y  0.0956

“H02” Cost from PBS

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

H02 %>% gg_season(Cost)

H02 %>% gg_subseries(Cost)

H02 %>% ACF(Cost)

## # A tsibble: 92 x 6 [1M]
## # Key:       Concession, Type, ATC1, ATC2 [4]
##    Concession   Type        ATC1  ATC2    lag   acf
##    <chr>        <chr>       <chr> <chr> <lag> <dbl>
##  1 Concessional Co-payments H     H02      1M 0.834
##  2 Concessional Co-payments H     H02      2M 0.679
##  3 Concessional Co-payments H     H02      3M 0.514
##  4 Concessional Co-payments H     H02      4M 0.352
##  5 Concessional Co-payments H     H02      5M 0.264
##  6 Concessional Co-payments H     H02      6M 0.219
##  7 Concessional Co-payments H     H02      7M 0.253
##  8 Concessional Co-payments H     H02      8M 0.337
##  9 Concessional Co-payments H     H02      9M 0.464
## 10 Concessional Co-payments H     H02     10M 0.574
## # ... with 82 more rows

us_gasoline

us_gasoline %>% autoplot(Barrels)

us_gasoline %>% gg_season(Barrels)

us_gasoline %>% gg_subseries(Barrels)

us_gasoline %>% gg_lag(Barrels)

us_gasoline %>% ACF(Barrels)

## # A tsibble: 31 x 2 [1W]
##      lag   acf
##    <lag> <dbl>
##  1    1W 0.893
##  2    2W 0.882
##  3    3W 0.873
##  4    4W 0.866
##  5    5W 0.847
##  6    6W 0.844
##  7    7W 0.832
##  8    8W 0.831
##  9    9W 0.822
## 10   10W 0.808
## # ... with 21 more rows

10 The following time plots and ACF plots correspond to four different time series. Your task is to match each time plot in the first row with one of the ACF plots in the second row.

1-B, 2-A, 3-, 4-C

11 The aus_livestock data contains the monthly total number of pigs slaughtered in Victoria, Australia, from Jul 1972 to Dec 2018. Use filter() to extract pig slaughters in Victoria between 1990 and 1995. Use autoplot() and ACF() for this data. How do they differ from white noise? If a longer period of data is used, what difference does it make to the ACF?

Victoria_Pig<- aus_livestock %>% 
                        filter(State == "Victoria", 
                               Animal == "Pigs", 
                               between(year(Month),1990,1995))
Victoria_Pig %>% ACF(Count) %>% autoplot()

Almost all of the spikes are out of the bounds which is confirming the series is not white noise.

12 Use the following code to compute the daily changes in Google closing stock prices.

dgoog <- gafa_stock %>%
  filter(Symbol == "GOOG", year(Date) >= 2018) %>%
  mutate(trading_day = row_number()) %>%
  update_tsibble(index = trading_day, regular = TRUE) %>%
  mutate(diff = difference(Close))

12.1 Why was it necessary to re-index the tsibble?

Because when we use a filter for the GOOG symbol, the interval for GOOG by Date will be chaotic and not the same for each row, so we need to change our index to use the row sequence number so that the interval for each row is the same

12.2 Plot these differences and their ACF.

google_stock <- gafa_stock %>%
                            filter(Symbol == "GOOG") %>%
                            mutate(trading_day = row_number()) %>%
                            update_tsibble(index = trading_day, regular = TRUE)

google_stock %>%
            ACF(difference(Close)) %>%
            autoplot()

12.3 Do the changes in the stock prices look like white noise?

There are total 30 lags, 5% of 30 is

5/100*30

## [1] 1.5

then, if there are more than 1.5 lags that out of the bound, the data series is not white noises.

From the plot above we can clearly see that there are 3 lags that out of the bound, then the data series is probably not white noise.

Econometrics

Assignment 5: Time Series

Julian Salomo

April 22, 2021

1 Use the help function to explore what the series gafa_stock, PBS, vic_elec and peltrepresent.

1.1 GAFA stock prices

1.2 Monthly Medicare Australia prescription data

1.3 Half-hourly electricity demand for Victoria, Australia

1.4 Pelt trading records

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

3.1 You can read the data into R with the following script:

3.2 Convert the data to time series

3.3 Construct time series plots of each of the three series

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

4.1 Install the `USgas` package.

4.2 Create a tsibble from us_total with year as the index and state as the key.

4.3 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).

5 Follow the instructions below:

5.1 Download `tourism.xlsx` here and read it into R using `readxl::read_excel()`.

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

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

5.4 Create a new tsibble which combines the Purposes and Regions, and just has total trips by State.

6 Create time plots of the following four time series: Bricks from aus_production, Lynx from pelt, Close from gafa_stock, Demand from vic_elec.

6.1 Use ? (or help()) to find out about the data in each series.

6.2 For the last plot, modify the axis labels and title.(Demand from vic_elec)

7 The aus_arrivals data set comprises quarterly international arrivals to Australia from Japan, New Zealand, UK and the US.

7.1 Use autoplot(), gg_season() and gg_subseries() to compare the differences between the arrivals from these four countries.

7.2 Can you identify any unusual observations?

8 Monthly Australian retail data is provided in aus_retail. Select one of the time series as follows (but choose your own seed value):

9 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 us_gasoline.

10 The following time plots and ACF plots correspond to four different time series. Your task is to match each time plot in the first row with one of the ACF plots in the second row.

12 Use the following code to compute the daily changes in Google closing stock prices.

12.1 Why was it necessary to re-index the tsibble?

12.2 Plot these differences and their ACF.

12.3 Do the changes in the stock prices look like white noise?

Econometrics

Assignment 5: Time Series

Julian Salomo

April 22, 2021

1 Use the help function to explore what the series gafa_stock, PBS, vic_elec and peltrepresent.

1.1 GAFA stock prices

1.2 Monthly Medicare Australia prescription data

1.3 Half-hourly electricity demand for Victoria, Australia

1.4 Pelt trading records

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

3.1 You can read the data into R with the following script:

3.2 Convert the data to time series

3.3 Construct time series plots of each of the three series

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

4.1 Install the USgas package.

4.2 Create a tsibble from us_total with year as the index and state as the key.

4.3 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).

5 Follow the instructions below:

5.1 Download tourism.xlsx here and read it into R using readxl::read_excel().

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

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

5.4 Create a new tsibble which combines the Purposes and Regions, and just has total trips by State.

6 Create time plots of the following four time series: Bricks from aus_production, Lynx from pelt, Close from gafa_stock, Demand from vic_elec.

6.1 Use ? (or help()) to find out about the data in each series.

6.2 For the last plot, modify the axis labels and title.(Demand from vic_elec)

7 The aus_arrivals data set comprises quarterly international arrivals to Australia from Japan, New Zealand, UK and the US.

7.1 Use autoplot(), gg_season() and gg_subseries() to compare the differences between the arrivals from these four countries.

7.2 Can you identify any unusual observations?

8 Monthly Australian retail data is provided in aus_retail. Select one of the time series as follows (but choose your own seed value):

9 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 us_gasoline.

10 The following time plots and ACF plots correspond to four different time series. Your task is to match each time plot in the first row with one of the ACF plots in the second row.

12 Use the following code to compute the daily changes in Google closing stock prices.

12.1 Why was it necessary to re-index the tsibble?

12.2 Plot these differences and their ACF.

12.3 Do the changes in the stock prices look like white noise?

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

4.1 Install the `USgas` package.

5.1 Download `tourism.xlsx` here and read it into R using `readxl::read_excel()`.

9 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 us_gasoline.