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R代写-TERM 1 2021

时间：2021-05-04

THE UNIVERSITY OF NEW SOUTH WALES

SCHOOL OF ECONOMICS

TERM 1 2021

ECON2209 BUSINESS FORECASTING

FINAL EXAMINATION

1. Time Allowed: 24 Hours.

2. This is a Take-Home Exam, your responses must be your own original work.

You must attempt this exam by yourself, without any help from others. By

submitting this exam, you are declaring that you have NOT worked,

collaborated, or colluded with any other persons in the formulation of your

responses. The work that you are submitting is your OWN work.

3. Release date/time (via Moodle)

Wednesday, 5 May 2021, 9:00am (Australian Eastern Standard Time)

4. Submission date/time (Via Turnitin):

Thursday, 6 May 2021, 9:00am (Australian Eastern Standard Time)

5. Failure to upload the exam by the submission time will result in an immediate

late penalty of five marks from 9:01am on 6 May, followed by additional

penalties of five marks per hour of lateness.

6. This Examination Paper has 6 pages: 2 cover pages and 4 pages with questions.

7. This Examination Paper has 2 parts.

8. Answer all three questions in Part A, and answer ONE of two questions in Part

B. If you answer both questions in Part B, only the first answered question will

be marked.

9. Total marks available: 55 marks. This examination is worth 55% of the total

marks for the course.

10. Questions are not of equal value. Marks available for question sub-parts are

shown on this exam paper.

11. This Take-Home Exam paper cannot be copied, forwarded or shared.

PAGE 2 OF 2

12. Students are reminded of UNSW’s rules regarding Academic Integrity and

Plagiarism. Plagiarism is a serious breach of ethics at UNSW and is not taken

lightly. For details see Examples of plagiarism.

13. This Take-Home Exam is an open book/open web exam. Further information is

available by clicking here.

• You are permitted to refer to your course notes, any materials provided by

the lecturer, books, journal articles, or tutorial materials.

• You are required to cite your sources and attribute direct quotes

appropriately when using external sources (other than your course

materials).

• It is sufficient to use in-text citations that include the following information:

the name of the author or authors; the year of publication; the page number

(where the information/idea can be located on a particular page when

directly quoted), For example, (McConville, 2011, p.188).

• When citing Internet sources, please use the following format: website/page

title and date.

• If you provide in-text citations, you MUST provide a Reference List.

14. Students are advised to read the exam paper thoroughly before commencing.

15. The Lecturer will be available online (via Moodle) after the exam paper is

released for a period of two hours.

UNSW ECON2209 Assessment

Final Exam

2021

Remember to type ‘library(fpp3)‘ in the R Studio Console before you start.

Part A: Answer all three questions

Question 1 [10 marks]

For this question, use the aus_accommodation tsibble as provided by the package fpp3. This has

the total quarterly takings from accommodation and the room occupancy level for hotels, motels,

and guest houses in Australia, between January 1998 and June 2016, along with Consumer Price

Index (CPI) data for each period. Total quarterly takings are in millions of Australian dollars.

a. [2 marks] Compute the CPI-adjusted takings for each state and territory and plot the

resulting series in one figure. Discuss the figure.

b. [3 marks] For New South Wales:

(i) Fit a dynamic regression model of CPI-adjusted takings with seasonal dummy

variables, a piecewise linear time trend with one knot at 2008 Q1, and ARIMA

errors.

(ii) Have the seasonal dummy variables adequately handled the seasonality?

(iii) Check if the errors are white noise.

c. [3 marks] Forecast the adjusted takings for NSW to the end of 2017 and discuss.

Hint: You will need to produce forecasts of the CPI first. How you do this is up to you.

d. [2 marks] What sources of uncertainty have not been taken into account in the prediction

intervals?

Question 2: [10 marks]

For your retail time series from the Course Project:

Develop an appropriate dynamic regression model with Fourier terms for the seasonality. Use

the AICc to select the number of Fourier terms to include in the model. (Use any appropriate

Box-Cox transformation you identified in the Course Project.) Describe your model, and check if

the residual series is white noise.

Hint: For each K, try including e.g. pdq(0:2, 0, 0:2) + PDQ(0:1, 0, 0:1) in your model

specification to help with quickly considering a lot of different models.

5 marks for fitting a sensible model, 5 marks for a sensible description and discussion.

1

Question 3 [20 marks]

This question uses data from the Australian Bureau of Statistics (ABS) on consumer prices, from ABS

Catalogue 6401.0, Consumer Price Index: https://www.abs.gov.au/statistics/economy/price-indexes-and-

inflation/consumer-price-index-australia/latest-release

If you haven’t done so already, install the package readabs:

install.packages("readabs")

Read in data from an Excel spreadsheet on the ABS website using the package and create a

tsibble, as follows:

library(readabs)

cpidata <- read_abs("6401.0", tables=5, check_local=FALSE) %>%

mutate ( Quarter = yearquarter (date)) %>%

as_tsibble (

index = Quarter,

key = c (series_id)

)

You must use the following method for selecting your data series.

Use the seven digits of your UNSW student ID to get the data series that you will analyse in this

question, as in the following example for the case when your student ID is z1234567:

Select your series by replacing “1234567” with the numbers of your student ID:

set.seed(1234567)

select_series <- cpidata %>%

filter (`series_id` == sample (cpidata$`series_id` , 1),

year(Quarter)>=1990)

Simplify the series description and plot your series using the following commands:

myseries <- select_series %>%

replace("series", sub("Index Numbers ;", "", select_series$series))

myseries %>%

autoplot(value) +

labs ( y = "Inflation Index" ,

title = myseries$series[1])

a. [5 marks] Explore your data series using the following functions, being sure to discuss what

you find:

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

What Box-Cox transformation, if any, would you select for your data?

b. [5 marks] For your untransformed data series, create a training dataset (myseries_train)

consisting of observations before 2013. Calculate seasonal naïve forecasts using SNAIVE()

applied to your training data and check the residuals. Produce forecasts for the test data.

Compare the accuracy of your forecasts against the actual values.

c. [5 marks] For your full, untransformed data series, apply Holt-Winters’ multiplicative

method to the data. Then try the method making the trend damped. Plot and compare the

12-period ahead point forecasts and prediction intervals for both methods. Using accuracy(),

compare the RMSE of the of the two methods; this comparison is based on one-step-ahead

in-sample forecasts. Which method do you prefer and why?

2

d. [5 marks] Train the model to the end of 2012 and find the test set RMSE. Compare the

RMSE with those from a (i) Holt-Winters’ multiplicative model, (i) seasonal naïve model (ii)

a drift model, and (iii) using any transformation previously found appropriate in part a, an

STL-ARIMA model. Discuss.

Part B: Answer ONLY ONE of the following questions

Question 4 [15 marks]

The data set souvenirs from the package fpp3 concerns the monthly sales figures of a shop

which opened in January 1987 and sells gifts, souvenirs, and novelties. The shop is situated on

the wharf at a beach resort town in Queensland, Australia. The sales volume varies with the

seasonal population of tourists. There is a large influx of visitors to the town at Christmas and

for the local surfing festival, held every March since 1988. Over time, the shop has expanded its

premises, range of products, and staff.

a. [5 marks] Fit a regression model to the logarithms of these sales data with a linear trend,

seasonal dummies and a “surfing festival” dummy variable. You will have to create this

dummy variable. Discuss the results.

b. [5 marks] What do the values of the coefficients on the trend, the February dummy, the

December dummy and the festival dummy tell you about the percentage impact on sales?

c. [5 marks] Use your regression model to predict the monthly sales for 1994, 1995, and

1996. Produce prediction intervals for your forecasts. Describe how you could improve these

predictions by modifying the model.

Question 5 [15 marks]

Electricity consumption is often modelled as a function of temperature. Temperature is measured

by daily heating degrees and cooling degrees. Heating degrees is 18◦C minus the average daily

temperature when the daily average is below 18◦C; otherwise it is zero. This provides a measure

of our need to heat ourselves as temperature falls. Cooling degrees measures our need to cool

ourselves as the temperature rises. It is defined as the average daily temperature minus 18◦C

when the daily average is above 18◦C; otherwise it is zero. Let yt denote the monthly total of

kilowatt-hours of electricity used, let x1,t denote the monthly total of heating degrees, and let x2,t

denote the monthly total of cooling degrees.

An analyst fits the following model to a set of such data:

y∗t = β1x∗1,t + β2x∗2,t + ηt,

where

(1−B)(1−B12)ηt = 1− θ1B1− φ12B12 − φ24B24 εt

and y∗t = log(yt), x∗1,t =

√

x1,t and x∗2,t =

√

x2,t.

a. [3 marks] What sort of ARIMA model has the analyst identified for ηt? (For example, is it

an ARIMA(1,0,0)(0,0,1)12 model?)

3

b. [2 marks] The estimated coefficients are

Parameter Estimate s.e. Z P -value

β1 0.0077 0.0015 4.98 0.000

β2 0.0208 0.0023 9.23 0.000

θ1 0.5830 0.0720 8.10 0.000

φ12 -0.5373 0.0856 -6.27 0.000

φ24 -0.4667 0.0862 -5.41 0.000

Explain what the estimates of β1 and β2 tell us about electricity consumption.

c. [5 marks] Write the equation in a form more suitable for forecasting. (Handwritten answers

are fine, but they must be embedded in the PDF file that is submitted.)

d. [3 marks] Describe how this model could be used to forecast electricity demand for the

next 12 months.

e. [2 marks} Explain why the ηt term should be modelled with an ARIMA model rather

than modelling the data using a standard ordinary least squares regression approach. In

your discussion, comment on the properties of the estimates, the validity of the standard

regression results, and the importance of the ηt model in producing forecasts.

4

学霸联盟

SCHOOL OF ECONOMICS

TERM 1 2021

ECON2209 BUSINESS FORECASTING

FINAL EXAMINATION

1. Time Allowed: 24 Hours.

2. This is a Take-Home Exam, your responses must be your own original work.

You must attempt this exam by yourself, without any help from others. By

submitting this exam, you are declaring that you have NOT worked,

collaborated, or colluded with any other persons in the formulation of your

responses. The work that you are submitting is your OWN work.

3. Release date/time (via Moodle)

Wednesday, 5 May 2021, 9:00am (Australian Eastern Standard Time)

4. Submission date/time (Via Turnitin):

Thursday, 6 May 2021, 9:00am (Australian Eastern Standard Time)

5. Failure to upload the exam by the submission time will result in an immediate

late penalty of five marks from 9:01am on 6 May, followed by additional

penalties of five marks per hour of lateness.

6. This Examination Paper has 6 pages: 2 cover pages and 4 pages with questions.

7. This Examination Paper has 2 parts.

8. Answer all three questions in Part A, and answer ONE of two questions in Part

B. If you answer both questions in Part B, only the first answered question will

be marked.

9. Total marks available: 55 marks. This examination is worth 55% of the total

marks for the course.

10. Questions are not of equal value. Marks available for question sub-parts are

shown on this exam paper.

11. This Take-Home Exam paper cannot be copied, forwarded or shared.

PAGE 2 OF 2

12. Students are reminded of UNSW’s rules regarding Academic Integrity and

Plagiarism. Plagiarism is a serious breach of ethics at UNSW and is not taken

lightly. For details see Examples of plagiarism.

13. This Take-Home Exam is an open book/open web exam. Further information is

available by clicking here.

• You are permitted to refer to your course notes, any materials provided by

the lecturer, books, journal articles, or tutorial materials.

• You are required to cite your sources and attribute direct quotes

appropriately when using external sources (other than your course

materials).

• It is sufficient to use in-text citations that include the following information:

the name of the author or authors; the year of publication; the page number

(where the information/idea can be located on a particular page when

directly quoted), For example, (McConville, 2011, p.188).

• When citing Internet sources, please use the following format: website/page

title and date.

• If you provide in-text citations, you MUST provide a Reference List.

14. Students are advised to read the exam paper thoroughly before commencing.

15. The Lecturer will be available online (via Moodle) after the exam paper is

released for a period of two hours.

UNSW ECON2209 Assessment

Final Exam

2021

Remember to type ‘library(fpp3)‘ in the R Studio Console before you start.

Part A: Answer all three questions

Question 1 [10 marks]

For this question, use the aus_accommodation tsibble as provided by the package fpp3. This has

the total quarterly takings from accommodation and the room occupancy level for hotels, motels,

and guest houses in Australia, between January 1998 and June 2016, along with Consumer Price

Index (CPI) data for each period. Total quarterly takings are in millions of Australian dollars.

a. [2 marks] Compute the CPI-adjusted takings for each state and territory and plot the

resulting series in one figure. Discuss the figure.

b. [3 marks] For New South Wales:

(i) Fit a dynamic regression model of CPI-adjusted takings with seasonal dummy

variables, a piecewise linear time trend with one knot at 2008 Q1, and ARIMA

errors.

(ii) Have the seasonal dummy variables adequately handled the seasonality?

(iii) Check if the errors are white noise.

c. [3 marks] Forecast the adjusted takings for NSW to the end of 2017 and discuss.

Hint: You will need to produce forecasts of the CPI first. How you do this is up to you.

d. [2 marks] What sources of uncertainty have not been taken into account in the prediction

intervals?

Question 2: [10 marks]

For your retail time series from the Course Project:

Develop an appropriate dynamic regression model with Fourier terms for the seasonality. Use

the AICc to select the number of Fourier terms to include in the model. (Use any appropriate

Box-Cox transformation you identified in the Course Project.) Describe your model, and check if

the residual series is white noise.

Hint: For each K, try including e.g. pdq(0:2, 0, 0:2) + PDQ(0:1, 0, 0:1) in your model

specification to help with quickly considering a lot of different models.

5 marks for fitting a sensible model, 5 marks for a sensible description and discussion.

1

Question 3 [20 marks]

This question uses data from the Australian Bureau of Statistics (ABS) on consumer prices, from ABS

Catalogue 6401.0, Consumer Price Index: https://www.abs.gov.au/statistics/economy/price-indexes-and-

inflation/consumer-price-index-australia/latest-release

If you haven’t done so already, install the package readabs:

install.packages("readabs")

Read in data from an Excel spreadsheet on the ABS website using the package and create a

tsibble, as follows:

library(readabs)

cpidata <- read_abs("6401.0", tables=5, check_local=FALSE) %>%

mutate ( Quarter = yearquarter (date)) %>%

as_tsibble (

index = Quarter,

key = c (series_id)

)

You must use the following method for selecting your data series.

Use the seven digits of your UNSW student ID to get the data series that you will analyse in this

question, as in the following example for the case when your student ID is z1234567:

Select your series by replacing “1234567” with the numbers of your student ID:

set.seed(1234567)

select_series <- cpidata %>%

filter (`series_id` == sample (cpidata$`series_id` , 1),

year(Quarter)>=1990)

Simplify the series description and plot your series using the following commands:

myseries <- select_series %>%

replace("series", sub("Index Numbers ;", "", select_series$series))

myseries %>%

autoplot(value) +

labs ( y = "Inflation Index" ,

title = myseries$series[1])

a. [5 marks] Explore your data series using the following functions, being sure to discuss what

you find:

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

What Box-Cox transformation, if any, would you select for your data?

b. [5 marks] For your untransformed data series, create a training dataset (myseries_train)

consisting of observations before 2013. Calculate seasonal naïve forecasts using SNAIVE()

applied to your training data and check the residuals. Produce forecasts for the test data.

Compare the accuracy of your forecasts against the actual values.

c. [5 marks] For your full, untransformed data series, apply Holt-Winters’ multiplicative

method to the data. Then try the method making the trend damped. Plot and compare the

12-period ahead point forecasts and prediction intervals for both methods. Using accuracy(),

compare the RMSE of the of the two methods; this comparison is based on one-step-ahead

in-sample forecasts. Which method do you prefer and why?

2

d. [5 marks] Train the model to the end of 2012 and find the test set RMSE. Compare the

RMSE with those from a (i) Holt-Winters’ multiplicative model, (i) seasonal naïve model (ii)

a drift model, and (iii) using any transformation previously found appropriate in part a, an

STL-ARIMA model. Discuss.

Part B: Answer ONLY ONE of the following questions

Question 4 [15 marks]

The data set souvenirs from the package fpp3 concerns the monthly sales figures of a shop

which opened in January 1987 and sells gifts, souvenirs, and novelties. The shop is situated on

the wharf at a beach resort town in Queensland, Australia. The sales volume varies with the

seasonal population of tourists. There is a large influx of visitors to the town at Christmas and

for the local surfing festival, held every March since 1988. Over time, the shop has expanded its

premises, range of products, and staff.

a. [5 marks] Fit a regression model to the logarithms of these sales data with a linear trend,

seasonal dummies and a “surfing festival” dummy variable. You will have to create this

dummy variable. Discuss the results.

b. [5 marks] What do the values of the coefficients on the trend, the February dummy, the

December dummy and the festival dummy tell you about the percentage impact on sales?

c. [5 marks] Use your regression model to predict the monthly sales for 1994, 1995, and

1996. Produce prediction intervals for your forecasts. Describe how you could improve these

predictions by modifying the model.

Question 5 [15 marks]

Electricity consumption is often modelled as a function of temperature. Temperature is measured

by daily heating degrees and cooling degrees. Heating degrees is 18◦C minus the average daily

temperature when the daily average is below 18◦C; otherwise it is zero. This provides a measure

of our need to heat ourselves as temperature falls. Cooling degrees measures our need to cool

ourselves as the temperature rises. It is defined as the average daily temperature minus 18◦C

when the daily average is above 18◦C; otherwise it is zero. Let yt denote the monthly total of

kilowatt-hours of electricity used, let x1,t denote the monthly total of heating degrees, and let x2,t

denote the monthly total of cooling degrees.

An analyst fits the following model to a set of such data:

y∗t = β1x∗1,t + β2x∗2,t + ηt,

where

(1−B)(1−B12)ηt = 1− θ1B1− φ12B12 − φ24B24 εt

and y∗t = log(yt), x∗1,t =

√

x1,t and x∗2,t =

√

x2,t.

a. [3 marks] What sort of ARIMA model has the analyst identified for ηt? (For example, is it

an ARIMA(1,0,0)(0,0,1)12 model?)

3

b. [2 marks] The estimated coefficients are

Parameter Estimate s.e. Z P -value

β1 0.0077 0.0015 4.98 0.000

β2 0.0208 0.0023 9.23 0.000

θ1 0.5830 0.0720 8.10 0.000

φ12 -0.5373 0.0856 -6.27 0.000

φ24 -0.4667 0.0862 -5.41 0.000

Explain what the estimates of β1 and β2 tell us about electricity consumption.

c. [5 marks] Write the equation in a form more suitable for forecasting. (Handwritten answers

are fine, but they must be embedded in the PDF file that is submitted.)

d. [3 marks] Describe how this model could be used to forecast electricity demand for the

next 12 months.

e. [2 marks} Explain why the ηt term should be modelled with an ARIMA model rather

than modelling the data using a standard ordinary least squares regression approach. In

your discussion, comment on the properties of the estimates, the validity of the standard

regression results, and the importance of the ηt model in producing forecasts.

4

学霸联盟