Data 624 HW01

Textbook: Hyndman, R.J., & Athanasopoulos, G. (2018) Forecasting: principles and practice, 2nd edition, OTexts: Melbourne, Australia.

Exercise 2.1 : Use the help function to explore what the series gold, woolyrnq and gas represent.

# load packages
library(fpp2)
library(ggplot2)

help(gold)

Description Daily morning gold prices in US dollars. 1 January 1985 – 31 March 1989.

help(woolyrnq)

Description Quarterly production of woollen yarn in Australia: tonnes. Mar 1965 – Sep 1994.

help(gas)

Description Australian monthly gas production: 1956–1995.

a) Use autoplot() to plot each of these in separate plots.

Gold

autoplot(gold) + 
   labs(title = "Daily Morning Gold Prices", subtitle = "1 Jan 1985 – 31 Mar 1989")+
   xlab("No of days") +
   ylab("USD")+
   theme_minimal()+
   theme(plot.title = element_text(hjust = 0.5), plot.subtitle = element_text(hjust = 0.5))+
   scale_y_continuous()

Woolyrnq

autoplot(woolyrnq) + 
   labs(title = "Quarterly Production woollen yarn Australia", subtitle = "Mar 1965 – Sep 1994")+
   xlab("Year") +
   ylab("tonnes")+
   theme_minimal()+
   theme(plot.title = element_text(hjust = 0.5), plot.subtitle = element_text(hjust = 0.5))

Gas

autoplot(gas) + 
   labs(title = "Australian monthly gas production", subtitle = "1956–1995")+
   xlab("Year") +
   ylab("Amount")+
   theme_minimal()+
   theme(plot.title = element_text(hjust = 0.5), plot.subtitle = element_text(hjust = 0.5))

b) What is the frequency of each series? Hint: apply the frequency() function.

sprintf('The frequency for the Gold time series data is %d (annual).', frequency(gold))

## [1] "The frequency for the Gold time series data is 1 (annual)."

sprintf("The frequency for the Woollen Yarn time series data is %d (quarterly).", frequency(woolyrnq))

## [1] "The frequency for the Woollen Yarn time series data is 4 (quarterly)."

sprintf("The frequency for the Gas time series data is %d (monthly).", frequency(gas))

## [1] "The frequency for the Gas time series data is 12 (monthly)."

c) Use which.max() to spot the outlier in the gold series. Which observation was it?

sprintf("A possible outlier in the gold series occurs on day %d, with a price of US$ %.2f.", which.max(gold), gold[which.max(gold)])

## [1] "A possible outlier in the gold series occurs on day 770, with a price of US$ 593.70."

Exercise 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.

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

tute1 <- read.csv("tute1.csv", header=TRUE)
head(tute1)

##        X  Sales AdBudget   GDP
## 1 Mar-81 1020.2    659.2 251.8
## 2 Jun-81  889.2    589.0 290.9
## 3 Sep-81  795.0    512.5 290.8
## 4 Dec-81 1003.9    614.1 292.4
## 5 Mar-82 1057.7    647.2 279.1
## 6 Jun-82  944.4    602.0 254.0

Convert the data to time series

mytimeseries <- ts(tute1[,-1], start=1981, frequency=4)

(The [,-1] removes the first column which contains the quarters as we don’t need them now.)

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)

All three are plotted on the same y axis. The seasonality in GDP is much harder to grasp in this case. The plots ate separated by colors as shown in the legend. I believe the plot where facets=TRUE shows the fluctuations and outlines the scales more clearly.

Exercise 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) You can read the data into R with the following script:

retaildata <- readxl::read_excel("retail.xlsx", skip=1)
head(retaildata)

## # A tibble: 6 x 190
##   `Series ID`         A3349335T A3349627V A3349338X A3349398A A3349468W
##   <dttm>                  <dbl>     <dbl>     <dbl>     <dbl>     <dbl>
## 1 1982-04-01 00:00:00      303.      41.7      63.9      409.      65.8
## 2 1982-05-01 00:00:00      298.      43.1      64        405.      65.8
## 3 1982-06-01 00:00:00      298       40.3      62.7      401       62.3
## 4 1982-07-01 00:00:00      308.      40.9      65.6      414.      68.2
## 5 1982-08-01 00:00:00      299.      42.1      62.6      404.      66  
## 6 1982-09-01 00:00:00      305.      42        64.4      412.      62.3
## # ... with 184 more variables: A3349336V <dbl>, A3349337W <dbl>,
## #   A3349397X <dbl>, A3349399C <dbl>, A3349874C <dbl>, A3349871W <dbl>,
## #   A3349790V <dbl>, A3349556W <dbl>, A3349791W <dbl>, A3349401C <dbl>,
## #   A3349873A <dbl>, A3349872X <dbl>, A3349709X <dbl>, A3349792X <dbl>,
## #   A3349789K <dbl>, A3349555V <dbl>, A3349565X <dbl>, A3349414R <dbl>,
## #   A3349799R <dbl>, A3349642T <dbl>, A3349413L <dbl>, A3349564W <dbl>,
## #   A3349416V <dbl>, A3349643V <dbl>, A3349483V <dbl>, A3349722T <dbl>,
## #   A3349727C <dbl>, A3349641R <dbl>, A3349639C <dbl>, A3349415T <dbl>,
## #   A3349349F <dbl>, A3349563V <dbl>, A3349350R <dbl>, A3349640L <dbl>,
## #   A3349566A <dbl>, A3349417W <dbl>, A3349352V <dbl>, A3349882C <dbl>,
## #   A3349561R <dbl>, A3349883F <dbl>, A3349721R <dbl>, A3349478A <dbl>,
## #   A3349637X <dbl>, A3349479C <dbl>, A3349797K <dbl>, A3349477X <dbl>,
## #   A3349719C <dbl>, A3349884J <dbl>, A3349562T <dbl>, A3349348C <dbl>,
## #   A3349480L <dbl>, A3349476W <dbl>, A3349881A <dbl>, A3349410F <dbl>,
## #   A3349481R <dbl>, A3349718A <dbl>, A3349411J <dbl>, A3349638A <dbl>,
## #   A3349654A <dbl>, A3349499L <dbl>, A3349902A <dbl>, A3349432V <dbl>,
## #   A3349656F <dbl>, A3349361W <dbl>, A3349501L <dbl>, A3349503T <dbl>,
## #   A3349360V <dbl>, A3349903C <dbl>, A3349905J <dbl>, A3349658K <dbl>,
## #   A3349575C <dbl>, A3349428C <dbl>, A3349500K <dbl>, A3349577J <dbl>,
## #   A3349433W <dbl>, A3349576F <dbl>, A3349574A <dbl>, A3349816F <dbl>,
## #   A3349815C <dbl>, A3349744F <dbl>, A3349823C <dbl>, A3349508C <dbl>,
## #   A3349742A <dbl>, A3349661X <dbl>, A3349660W <dbl>, A3349909T <dbl>,
## #   A3349824F <dbl>, A3349507A <dbl>, A3349580W <dbl>, A3349825J <dbl>,
## #   A3349434X <dbl>, A3349822A <dbl>, A3349821X <dbl>, A3349581X <dbl>,
## #   A3349908R <dbl>, A3349743C <dbl>, A3349910A <dbl>, A3349435A <dbl>,
## #   A3349365F <dbl>, A3349746K <dbl>, ...

The second argument (skip=1) is required because the Excel sheet has two header rows.

b) Select one of the time series as follows (but replace the column name with your own chosen column):

myts <- ts(retaildata[,"A3349873A"],
  frequency=12, start=c(1982,4))
head(myts, 20)

##        Jan   Feb   Mar   Apr   May   Jun   Jul   Aug   Sep   Oct   Nov   Dec
## 1982                    62.4  63.1  59.6  61.9  60.7  61.2  62.1  68.3 104.0
## 1983  63.9  64.8  70.0  65.3  68.9  65.7  66.9  70.4  71.6  74.9  83.4

c) Explore your chosen retail time series using the following functions.

autoplot(), ggseasonplot(), ggsubseriesplot(), gglagplot(), ggAcf()

autoplot(myts)+
   labs(title = "Autoplot for Retail Sales ")+
   xlab("Year") +
   ylab("Sales")+
   theme_minimal()+
   theme(plot.title = element_text(hjust = 0.5))

ggseasonplot(myts)+
   labs(title = "Seasonplot for Retail Sales ")+
   xlab("Year") +
   ylab("Sales")+
   theme_minimal()+
   theme(plot.title = element_text(hjust = 0.5))

ggsubseriesplot(myts)+
   labs(title = "Subseries plot for Retail Sales ")+
   xlab("Year") +
   ylab("Sales")+
   theme_minimal()+
   theme(plot.title = element_text(hjust = 0.5))

gglagplot(myts)+
   labs(title = "Lagplot for Retail Sales ")+
   xlab("Year") +
   ylab("Sales")+
   theme_minimal()+
   theme(plot.title = element_text(hjust = 0.5))

ggAcf(myts)+
   labs(title = "ACF Retail Sales ")+
   xlab("Year") +
   ylab("Sales")+
   theme_minimal()+
   theme(plot.title = element_text(hjust = 0.5))

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

The autoplot shows an uptrend in sales.

The seasonal plot shows seasonality in the months March, May, and July, and in the quarter Oct-Dec, when sales tend to go up compared to the rest of the months.

The subseries plot shows that there are more sales in November and significantly higher mean sales in DEcmeber.

The lagplot shows that there is a strong upward positive reationship at lag 12.

The acf plot shows a slow decrease in the ACF as the lags increase is due to the trend, while the “scalloped” shape is due the seasonality.R12 and R24 are much higher than the other lags as Decemeber sales are significantly higher.

Exercise 2.6 : Use the following graphics functions: `autoplot()`, `ggseasonplot()`, `ggsubseriesplot()`, `gglagplot()`, `ggAcf()` and explore features from the following time series: `hsales`, `usdeaths`, `bricksq`, `sunspotarea`, `gasoline`.

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

hsales-Sales of one-family houses

autoplot(hsales)+
   labs(title = "Autoplot ")+
   xlab("Year") +
   ylab("Sales")+
   theme_minimal()+
   theme(plot.title = element_text(hjust = 0.5))

ggseasonplot(hsales)+
   labs(title = "Seasonplot ")+
   xlab("Year") +
   ylab("Sales")+
   theme_minimal()+
   theme(plot.title = element_text(hjust = 0.5))

ggsubseriesplot(hsales)+
   labs(title = "Subseries plot ")+
   xlab("Year") +
   ylab("Sales")+
   theme_minimal()+
   theme(plot.title = element_text(hjust = 0.5))

gglagplot(hsales)+
   labs(title = "Lagplot  ")+
   xlab("Year") +
   ylab("Sales")+
   theme_minimal()+
   theme(plot.title = element_text(hjust = 0.5))

ggAcf(hsales)+
   labs(title = "ACF Plot ")+
   xlab("Year") +
   ylab("Sales")+
   theme_minimal()+
   theme(plot.title = element_text(hjust = 0.5))

The data shows both seasonal and cyclic patterns,but there is no evidence of a trend. The seasonality peaks in March, and tapers off until July. The autoplot shows a couple of down cycles in the early 80s and 90s, and up cycles in late 70s, 80s and 90s. The lag plots show that there is a positive autocorrelation in lag 1 only.The Acf shows this is not a white noise series with a lot of the bars going beyond the autocorrelation bounds.

usdeaths - Accidental deaths in USA

autoplot(usdeaths)+
   labs(title = "Autoplot ")+
   xlab("Year") +
   ylab("No of deaths")+
   theme_minimal()+
   theme(plot.title = element_text(hjust = 0.5))

ggseasonplot(usdeaths)+
   labs(title = "Seasonplot ")+
   xlab("Year") +
   ylab("No of deaths")+
   theme_minimal()+
   theme(plot.title = element_text(hjust = 0.5))

ggsubseriesplot(usdeaths)+
   labs(title = "Subseries plot ")+
   xlab("Year") +
   ylab("No of deaths")+
   theme_minimal()+
   theme(plot.title = element_text(hjust = 0.5))

gglagplot(usdeaths)+
   labs(title = "Lagplot  ")+
   xlab("Year") +
   ylab("No of deaths")+
   theme_minimal()+
   theme(plot.title = element_text(hjust = 0.5))

ggAcf(usdeaths)+
   labs(title = "ACF Plot ")+
   xlab("Year") +
   ylab("No of deaths")+
   theme_minimal()+
   theme(plot.title = element_text(hjust = 0.5))

There is strong seasonality, but no trend and cyclicity can be seen. There seems to be a spike in deaths during the middle of the year. The lag plots show that there is a strong, positive autocorrelation in lag 12. The Acf shows 15 out of 24 lags beyond the autocorrelation boundaries so this is not a white noise series.

bricksq - Quarterly clay brick production

autoplot(bricksq)+
   labs(title = "Autoplot ")+
   xlab("Year") +
   ylab("No of units produced")+
   theme_minimal()+
   theme(plot.title = element_text(hjust = 0.5))

ggseasonplot(bricksq)+
   labs(title = "Seasonplot ")+
   xlab("Year") +
   ylab("No of units produced")+
   theme_minimal()+
   theme(plot.title = element_text(hjust = 0.5))

ggsubseriesplot(bricksq)+
   labs(title = "Subseries plot ")+
   xlab("Year") +
   ylab("No of units produced")+
   theme_minimal()+
   theme(plot.title = element_text(hjust = 0.5))

gglagplot(bricksq)+
   labs(title = "Lagplot  ")+
   xlab("Year") +
   ylab("No of units produced")+
   theme_minimal()+
   theme(plot.title = element_text(hjust = 0.5))

ggAcf(bricksq)+
   labs(title = "ACF Plot ")+
   xlab("Year") +
   ylab("No of units produced")+
   theme_minimal()+
   theme(plot.title = element_text(hjust = 0.5))

There is an upward trend and we can see dips every 3-5 years suggesting a cyclic pattern. There is seasonality with Q1 having the lowest and Q3 having the highest production levels. The data exhibits strong autocorrelation in lags 1 and 4. The Acf shows only positive autocorrelation for the lags, and the slow decrease in the ACF is due to the trend.The scallops are due to the seasonality.

sunspotarea - Annual average sunspot area

autoplot(sunspotarea)+
   labs(title = "Autoplot ")+
   xlab("Year") +
   ylab("Area")+
   theme_minimal()+
   theme(plot.title = element_text(hjust = 0.5))

#ggseasonplot(sunspotarea)+
  # labs(title = "Seasonplot")
   #xlab("Year") +
   #ylab("Area")+
   #theme_minimal()+
   #theme(plot.title = element_text(hjust = 0.5))
#ggsubseriesplot(sunspotarea)+
 #  labs(title = "Subseries plot ")+
  # xlab("Year") +
   #ylab("Area")+
   #theme_minimal()+
   #theme(plot.title = element_text(hjust = 0.5))
gglagplot(sunspotarea)+
   labs(title = "Lagplot  ")+
   xlab("Year") +
   ylab("Area")+
   theme_minimal()+
   theme(plot.title = element_text(hjust = 0.5))

ggAcf(sunspotarea)+
   labs(title = "ACF Plot ")+
   xlab("Year") +
   ylab("Area")+
   theme_minimal()+
   theme(plot.title = element_text(hjust = 0.5))

There is no indication of seasonality. Because of how the data was recorded, the seasonal and subseries plots could not be plotted. There is no clear trend but there seems to be upward and downward swings occurring over a period of 11 years.. The ACF shows this is not a white noise series.

gasoline - US finished motor gasoline product supplied

autoplot(gasoline)+
   labs(title = "Autoplot ")+
   xlab("Week") +
   ylab("No of units Supplied")+
   theme_minimal()+
   theme(plot.title = element_text(hjust = 0.5))

ggseasonplot(gasoline)+
   labs(title = "Seasonplot ")+
   xlab("Week") +
   ylab("No of units Supplied")+
   theme_minimal()+
   theme(plot.title = element_text(hjust = 0.5))

#ggsubseriesplot(gasoline)+
 #  labs(title = "Subseries plot ")+
  # xlab("Week") +
   #ylab("No of units Supplied")+
   #theme_minimal()+
   #theme(plot.title = element_text(hjust = 0.5))
gglagplot(gasoline)+
   labs(title = "Lagplot  ")+
   xlab("Week") +
   ylab("No of units Supplied")+
   theme_minimal()+
   theme(plot.title = element_text(hjust = 0.5))

ggAcf(gasoline)+
   labs(title = "ACF Plot ")+
   xlab("Week") +
   ylab("No of units Supplied")+
   theme_minimal()+
   theme(plot.title = element_text(hjust = 0.5))

The data exhibits a clear upward trend. The seasonal plot shows some seasonality depending on the week of the year, there is peak supply during the summer months with drop offs in the late fall and winter months. There is no noticeable cyclic pattern. The Acf shows this is not a white noise series. There are scallops in the Acf depicting the seasonality.

Data 624 HW01

Farhana Zahir

2/14/2021

Exercise 2.1 : Use the help function to explore what the series gold, woolyrnq and gas represent.

a) Use autoplot() to plot each of these in separate plots.

b) What is the frequency of each series? Hint: apply the frequency() function.

Exercise 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) You can read the data into R with the following script:

b) Select one of the time series as follows (but replace the column name with your own chosen column):

c) Explore your chosen retail time series using the following functions.

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

Exercise 2.6 : Use the following graphics functions: `autoplot()`, `ggseasonplot()`, `ggsubseriesplot()`, `gglagplot()`, `ggAcf()` and explore features from the following time series: `hsales`, `usdeaths`, `bricksq`, `sunspotarea`, `gasoline`.

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

Data 624 HW01

Farhana Zahir

2/14/2021

Exercise 2.1 : Use the help function to explore what the series gold, woolyrnq and gas represent.

a) Use autoplot() to plot each of these in separate plots.

b) What is the frequency of each series? Hint: apply the frequency() function.

Exercise 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) You can read the data into R with the following script:

b) Select one of the time series as follows (but replace the column name with your own chosen column):

c) Explore your chosen retail time series using the following functions.

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

Exercise 2.6 : Use the following graphics functions: autoplot(), ggseasonplot(), ggsubseriesplot(), gglagplot(), ggAcf() and explore features from the following time series: hsales, usdeaths, bricksq, sunspotarea, gasoline.

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

Exercise 2.6 : Use the following graphics functions: `autoplot()`, `ggseasonplot()`, `ggsubseriesplot()`, `gglagplot()`, `ggAcf()` and explore features from the following time series: `hsales`, `usdeaths`, `bricksq`, `sunspotarea`, `gasoline`.