Statistical Time Series CW2 2020
FEEDBACKS:
Q1: 4+ 11+6+4=25
Q2: 5+ 8+5+4+4=26
Q3: 9+10+5+3+1+2=30
Total: 81%, Excellent work
What you did well in this assignment:Please see the annotations in the pdf file.
What you could improve in this assignment: Please see the annotations & the
comments in “Post It” in the pdf file.
What you can take forward to your next assignment: Very good knowledge and skills
to analyse Time Series data using, Decomposition method, Exponential smoothing
method and Dummy variable regression techniques.
, Statistical Time Series CW2 2020
FEEDBACKS:
Q1: 4+ 11+6+4=25
Q2: 5+ 8+5+4+4=26
Q3: 9+10+5+3+1+2=30
Total: 81%, Excellent work
What you did well in this assignment:Please see the annotations in the pdf file.
What you could improve in this assignment: Please see the annotations & the
comments in “Post It” in the pdf file.
What you can take forward to your next assignment: Very good knowledge and skills
to analyse Time Series data using, Decomposition method, Exponential smoothing
method and Dummy variable regression techniques.
, STAT1041 Statistical Data Analysis and Time Series CW 2 2019/20
Topic: Time Series Analysis (Term 2)
Contribution: 25% Due in: 26/03/2020
Q1]. [30%]
Data on quarterly electricity sales revenue (in million £) of an electricity company
during a period of 6 years from 2014 to 2019 are given below.
Quarter 2014 2015 2016 2017 2018 2019
1 172 169 182 169 179 170
2 227 218 218 245 235 241
3 310 309 313 299 292 307
4 222 209 224 221 213 217
Table 1: Quarterly Electricity Sales
(a) Draw a time series plot and comment on any noticeable patterns in the series.
[4 marks]
(b) Suggest an appropriate time series model for the data, giving your reasons for choosing
this model. Describe your model and obtain estimates of the components of the model
using the decomposition method. You may use Excel in your calculations, but must
hand in a clear readable version of your worksheet output and the formulae.
[12 marks]
(c) Using your model forecast the company's sales for the four quarters of 2020.
Show clearly your calculations. What can be said about the expected accuracy of your
forecast?
[9 marks]
(d) On the basis of your model in part (b), compare and contrast the decomposition
method with the exponential smoothing method in time series analysis. You are not
required to do any calculations for this part.
[5 marks]
Q2]. [30%]
Metro Estate Agency operates several offices in a large city, specialising in property
sales and lettings. The company has grown rapidly over the last year or so and has been
expanding its business to accommodate the increasing demand for its services. As an
aid in planning, a forecast of the next three months' revenue is needed each month.
Revenue data (in £100) for the last 17 months are given below.
Month t 1 2 3 4 5 6 7 8 9
Revenue Yt 999 1123 1503 1762 2126 2315 2239 2655 2787
Month t 10 11 12 13 14 15 16 17 -
Revenue Yt 3024 3467 3528 3441 3588 3746 3628 4021 -
Table 2: Monthly revenue of Metro Estate Agency
, a) Plot the time series and discuss why Holt's two parameter method would be
appropriate for forecasting monthly revenue of Metro Estate Agency.
[6 marks]
b) Using the initial values m0=900, b0=180 and smoothing constants α=0.2, β=0.3 carry
out double exponential smoothing (Holt's method) in Excel and forecast the company’s
revenue for the next three months. Hand in all your Excel work (clear readable version),
including formulae, with your coursework.
[8 marks]
c) Superimpose the smoothed estimate of the mean mt on your time series plot and
comment on how the estimated mean recaptures the data. Hand in all your Excel work
with your coursework.
[6 marks]
d) Plot the successive one-period-ahead predictions on the time series plot and comment
on how well they capture the features in the observed data. Hand in all your Excel work
with your coursework.
[6 marks]
e) If the revenue for the month 18 were £410,000 what would be your revised forecast for
the next two months? Give details of your calculations.
[4 marks]
Q3]. [40%]
Quarterly profits, Yt, (in million £) made by a manufacturing firm for the past five years
are given in the following Table.
Quarter 2015 2016 2017 2018 2019
Q1 Y1 38 40 41 43
Q2 34 36 38 45 42
Q3 40 38 45 46 50
Q4 52 55 53 54 Y20
Table 3: Quarterly profit in million pounds
You must select your own values of Y1 and Y20 randomly from below.
Possible values for Y1 are [35, 35.5, 36, 36.5, 37, 37.5, 38, 38.5, 39, 39.5, 40]
Possible values for Y20 are [55, 55.5, 56, 56.5, 57, 57.5, 58, 58.5, 59, 59.5, 60]
To analyse this data, a time series model containing trend and seasonality is proposed.
(a) Describe fully an appropriate dummy variable regression model to analyse the time
series. Specify the assumptions involved in fitting the model and discuss how they can
be checked graphically.
[10 marks]
FEEDBACKS:
Q1: 4+ 11+6+4=25
Q2: 5+ 8+5+4+4=26
Q3: 9+10+5+3+1+2=30
Total: 81%, Excellent work
What you did well in this assignment:Please see the annotations in the pdf file.
What you could improve in this assignment: Please see the annotations & the
comments in “Post It” in the pdf file.
What you can take forward to your next assignment: Very good knowledge and skills
to analyse Time Series data using, Decomposition method, Exponential smoothing
method and Dummy variable regression techniques.
, Statistical Time Series CW2 2020
FEEDBACKS:
Q1: 4+ 11+6+4=25
Q2: 5+ 8+5+4+4=26
Q3: 9+10+5+3+1+2=30
Total: 81%, Excellent work
What you did well in this assignment:Please see the annotations in the pdf file.
What you could improve in this assignment: Please see the annotations & the
comments in “Post It” in the pdf file.
What you can take forward to your next assignment: Very good knowledge and skills
to analyse Time Series data using, Decomposition method, Exponential smoothing
method and Dummy variable regression techniques.
, STAT1041 Statistical Data Analysis and Time Series CW 2 2019/20
Topic: Time Series Analysis (Term 2)
Contribution: 25% Due in: 26/03/2020
Q1]. [30%]
Data on quarterly electricity sales revenue (in million £) of an electricity company
during a period of 6 years from 2014 to 2019 are given below.
Quarter 2014 2015 2016 2017 2018 2019
1 172 169 182 169 179 170
2 227 218 218 245 235 241
3 310 309 313 299 292 307
4 222 209 224 221 213 217
Table 1: Quarterly Electricity Sales
(a) Draw a time series plot and comment on any noticeable patterns in the series.
[4 marks]
(b) Suggest an appropriate time series model for the data, giving your reasons for choosing
this model. Describe your model and obtain estimates of the components of the model
using the decomposition method. You may use Excel in your calculations, but must
hand in a clear readable version of your worksheet output and the formulae.
[12 marks]
(c) Using your model forecast the company's sales for the four quarters of 2020.
Show clearly your calculations. What can be said about the expected accuracy of your
forecast?
[9 marks]
(d) On the basis of your model in part (b), compare and contrast the decomposition
method with the exponential smoothing method in time series analysis. You are not
required to do any calculations for this part.
[5 marks]
Q2]. [30%]
Metro Estate Agency operates several offices in a large city, specialising in property
sales and lettings. The company has grown rapidly over the last year or so and has been
expanding its business to accommodate the increasing demand for its services. As an
aid in planning, a forecast of the next three months' revenue is needed each month.
Revenue data (in £100) for the last 17 months are given below.
Month t 1 2 3 4 5 6 7 8 9
Revenue Yt 999 1123 1503 1762 2126 2315 2239 2655 2787
Month t 10 11 12 13 14 15 16 17 -
Revenue Yt 3024 3467 3528 3441 3588 3746 3628 4021 -
Table 2: Monthly revenue of Metro Estate Agency
, a) Plot the time series and discuss why Holt's two parameter method would be
appropriate for forecasting monthly revenue of Metro Estate Agency.
[6 marks]
b) Using the initial values m0=900, b0=180 and smoothing constants α=0.2, β=0.3 carry
out double exponential smoothing (Holt's method) in Excel and forecast the company’s
revenue for the next three months. Hand in all your Excel work (clear readable version),
including formulae, with your coursework.
[8 marks]
c) Superimpose the smoothed estimate of the mean mt on your time series plot and
comment on how the estimated mean recaptures the data. Hand in all your Excel work
with your coursework.
[6 marks]
d) Plot the successive one-period-ahead predictions on the time series plot and comment
on how well they capture the features in the observed data. Hand in all your Excel work
with your coursework.
[6 marks]
e) If the revenue for the month 18 were £410,000 what would be your revised forecast for
the next two months? Give details of your calculations.
[4 marks]
Q3]. [40%]
Quarterly profits, Yt, (in million £) made by a manufacturing firm for the past five years
are given in the following Table.
Quarter 2015 2016 2017 2018 2019
Q1 Y1 38 40 41 43
Q2 34 36 38 45 42
Q3 40 38 45 46 50
Q4 52 55 53 54 Y20
Table 3: Quarterly profit in million pounds
You must select your own values of Y1 and Y20 randomly from below.
Possible values for Y1 are [35, 35.5, 36, 36.5, 37, 37.5, 38, 38.5, 39, 39.5, 40]
Possible values for Y20 are [55, 55.5, 56, 56.5, 57, 57.5, 58, 58.5, 59, 59.5, 60]
To analyse this data, a time series model containing trend and seasonality is proposed.
(a) Describe fully an appropriate dummy variable regression model to analyse the time
series. Specify the assumptions involved in fitting the model and discuss how they can
be checked graphically.
[10 marks]
