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BU5562 Final Assignment for Part 1 (Time Series Econometrics)


University of Aberdeen Session 2021-2022
Alternative Assessment 1 for the Degree of MSc
BU5562 – Empirical Methods in Energy Economics
Wednesday 9th March 2022, 12:00 noon – Wednesday 30th March 2022, 12:00 noon
Online




RUBRIC: PLEASE READ WITH CARE

This Alternative Assessment lasts for THREE WEEKS.




Please submit your answer to the SafeAssign submission link on My Aberdeen within the
course BU5562 no later than 12:00 noon (UK time) on Wednesday 30th March 2022.

Do not include your name in your submission, only your Student ID number.


Late submissions will not be marked.


Please note that the university regulations on academic misconduct still apply
irrespective of the format the assessment is delivered.

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BU5562 Final Assignment for Part 1 (Time Series Econometrics)




Empirical Methods in Energy Economics
Module – BU5562
The Final Assessment Assignment for Part 1
(Time Series Econometrics)
Please note:
• This assignment consists of two sections, A and B.

• Section A comprises 2 questions both of which you must answer. Each
question has 20 marks (out of100).
• Section B requires you to work with a dataset made available in an excel file “Crude
Oil and Product Prices.xlsx” which can be found in the Assessment folder at the
course’s site at MyAberdeen or, BU5562 Class 2021-2022 MS Teams site. You
should load it onto the EViews software and use it to answer all relevant questions.
Each question has a given mark which add up to 60 marks (out of100). You must
answer all the questions in this Section.
• Please prepare your answer as a MS Word document structured as follows:
(a) Use the MS Word “Insert Page Number” facility to place the page numbers
sequentially at the top of each page (the same as this document).
(b) Use font size 12 and font type Arial throughout the document, and use the MS
Word equation facility for writing any mathematical notation or equation,
e.g., t = + t + t [to use this, you need to choose INSERT > Equation].
(c) Give your matriculation number at the top of each page.
(d) Answer each part of each question by starting a fresh page: copy and paste the
question you are answering at the top of the page (as the first paragraph) and
below it write down your answer, e.g., your answer to A1.1 should start on a
fresh page with the following paragraph, which is then followed by your answer to
it.
(A1.1) Describe the main features of the series.

(e) Your answers to Section B questions should consist of your explanations and the
relevant EViews outputs; please copy and paste, or put a screen shot of the
relevant output from the Eviews workfile (e.g., a plot, a table of regression
results, a table of statistics, etc.), put a heading for each piece of output and
number them sequentially, e.g., “Figure 1: Plot of x and y”. If you use the “print
screen” facility and include a screen shot image, please ensure you crop and
resize it properly so that only the relevant part is displayed, and the image is
clear and easily legible.
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BU5562 Final Assignment for Part 1 (Time Series Econometrics)




Section A: Answer all parts of both questions in this section
Question A1

Consider the series plotted in the graph below:



(A1.1) A time series typically has three main components. Explain what these are. (4 marks)
(A1.2) Describe the main features of the series in the above figure. (4 marks)
(A1.3) Explain if the series in the above figure is seasonal or not. How would you support your
answer with statistical evidence? (4 marks)
(A1.4) Explain if the series in the above figure has any deterministic trend or not. How would
you support your answer with statistical evidence? (4 marks)
(A1.5) Explain if the series in the above figure has any stochastic trend or not. How would you
support your answer with statistical evidence? (4 marks)



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BU5562 Final Assignment for Part 1 (Time Series Econometrics)


Question A2

Time series modelling attempts to model and predict variables using only information contained
in their own past values and, possibly current and past values of an error term. This practice can
be contrasted with structural modelling, where dependent variables are explained by
independent variables.

(A2.1) Suppose we model the data (not necessarily any of the series in Question A1) as an MA(1) and get the following estimated equation:

= 0.5−1+

What is this MA(1) process’ theoretical ACF at lag 1? At lag 2? Discuss the ACF and
PACF of general MA, AR, and ARMA processes. Why are we interested in measures
like ACF? In univariate time series modelling, how can measures like ACF and PACF
be used? Discuss in practice how to select the optimal lag length in time series
modelling.
(4 marks)

(A2.2) Univariate time series models are especially useful when it comes to forecasting.
Consider the following MA(1) process:

= 0.5−1+

What is your forecast for +1 if you observe −1 = 0.2 and = -0.8? What is your
forecast for +2? What is the forecast for 10-step ahead? How does the forecast for the
distant future compare to the unconditional expectation of this MA(1) process? How is
the forecasting exercise related to the expectation of the stochastic process {}?
(4 marks)

(A2.3) Distinguish between “in-sample forecasts” and “out-of-sample forecasts”. Which one is
closer to the true forecasting, where we make forecast of tomorrow based on the
information available until today?
(6 marks)

(A2.4) Suppose you are interested in forecasting the WTI spot price, how would you construct
the model?
Please report your results (in maximum 1000 words), including (not restricted to) the
following:
• Discussion of the data (length, frequency, source, etc).
• Discussion of what you expect and why?
• Explain the pre-treatment(s) of the data, if necessary.
• Construct a model for the WTI spot price.
• How is the model forecasting precision?

Please include all equations, figures, and tables necessary with your explanation
in your report..
(6 marks)
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BU5562 Final Assignment for Part 1 (Time Series Econometrics)





End of Section A
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BU5562 Final Assignment for Part 1 (Time Series Econometrics)






Section B: Answer all parts of all the 6 questions in this section


Data Source: http://www.eia.gov/dnav/pet/pet_pri_spt_s1_m.htm

The dataset for this part is taken from the above source (worksheets named Data 1 (column
B) and Data 2 (column C)) and is made available in an excel file “Crude Oil and Product
Prices.xlsx”, uploaded onto the Assessment folder at MyAberdeen and BU5562 Class 2021-
2022 MS Teams site. The file includes not-seasonally-adjusted observations on the WTI spot
prices (FOB) of crude oil (in US$/barrel) and US Gulf Coast Conventional Gasoline Regular (in
US$/gallon). Load the series into EViews, structure it according to the information provided
in the file, and rename the series as follows: crude oil price = x and gasoline price = y.

Save the EViews file and attempt the following questions. It is important that you accomplish
the above step 100% correctly; otherwise, Section B of your assignment will not be
considered, and you will lose the whole of 60 marks.


(B1) Plot y and x on the same graph and explain whether these series exhibit any distinct
patterns over the sample period. (2 marks)

(B2) Generate the logarithmic transformation of the two series and call them l_y and l_x.
Plot these on the same graph, inspect the plot carefully and explain whether the
logarithmic transformation changes the properties of the series in any way and, if so,
what is precisely the change you detect. Hence, stating your reasons clearly, explain
whether you prefer to use y and x or l_y and l_x when modelling the relationship
between the two series.
(2 marks)

Based on your answer to question (B2) above, answer the following questions using the
version of the series you prefer to use, e.g., if your answer suggests that you prefer to use y
and x then use those in answering the questions below.

(B3) Some researches have argued that both series, i.e. crude oil prices and gasoline prices,
are (a) integrated of order one, I(1); and (b) first-difference stationary. Provide statistical
evidence to check that each of these two assertions holds. (8 marks)

(B4) Several studies have proposed that the relationship between crude oil prices and gasoline
prices should be dynamic because changes in the latter take time to respond to changes
in the former. Based on the evidence that you have provided in your answer to (B3)
above, explain how you would formulate a dynamic regression equation that could be
used to test the above proposition. (8 marks)
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BU5562 Final Assignment for Part 1 (Time Series Econometrics)



(B5) Now, restrict the sample to 1990 to 2020 and attempt the following:
(B5.1) Estimate a DL(2) model that relates the change in l_y to the change in l_x,
comment on the results, and explain whether they support the above-mentioned
proposition about the dynamic nature of the relationship. (8 marks)
(B5.2) Estimate a DL(1) model that relates the change in l_y to the change in l_x,
comment on the results, and compare its statistical performance with that of the DL(2) model you obtained above. (8 marks)
(B5.3) Estimate an ARDL(1,1) model that relates the change in l_y to the change in l_x, comment on the results and compare its statistical performance with that of
DL(1) model you obtained above. (8 marks)
(B5.4) Use the evidence from these three regressions to support your preferred dynamic
relationship in this context. (8 marks)

(B6) There has been claims in the literature that the two series, i.e., crude oil prices and
gasoline prices, are likely to be cointegrated. Discuss the nature of the cointegration
relationship (if any) between them, with particular emphasis on which one should be
treated as the dependent variable and why. Estimate the cointegration relationship for
the sub-sample 1990 to 2020 and use it to verify statistically if the cointegration claim
holds for your proposed relationship. (8 marks)


End of Section B