CITY UNIVERSITY OF HONG KONG
SDSC6016 (Semester B, 2021)
Midterm Exam
Name:
Student ID:
Instructions (IMPORTANT - please read):
• You have 1.5 hours to complete this exam and additional 15 minutes
to submit.
• You need to make the submission on Canvas at/before 8:45pm on 9
March 2022. You need to upload your answers and the cover page
containing your name and student ID in one .pdf, .jpg or .doc file to
Canvas. If you experience diculty with Canvas, please email your sub-
mission to one of xiaoqiao@cityu.edu.hk, tyzhang25-c@my.cityu.edu.hk,
zonghao.y@my.cityu.edu.hk as a backup option.
• There are two parts in total. In multiple choice questions, please select
the most appropriate one. In short answer questions, please include
necessary procedure and explanation of your results.
• This is an open-book examination. Only lecture notes and scien-
tific calculators are allowed. Materials/aids other than lecture notes
are not permitted. Students will be subject to disciplinary action if any
unauthorized materials or aids are found on them.
• You can also reach the lecturer via Zoom/email for clarifying question(s)
during the exam.
1
Academic Honesty
The University requires all students to comply with the Rules on Academic
Honesty and regulations promulgated by the University and the academic
units in examinations and coursework. Students are reminded of the impor-
tance of academic honesty and the honesty pledge made when joining CityU.
Failure to adhere to the honesty pledge may have serious consequences.
“I pledge that the answers in this exam are my own and that I will not seek
or obtain an unfair advantage in producing these answers. Specifically,
• I will not plagiarize (copy without citation) from any source;
• I will not communicate or attempt to communicate with any other person
during the exam; neither will I give or attempt to give assistance to
another student taking the exam; and
• I will use only approved devices (e.g., calculators) and/or approved device
models
• I understand that any act of academic dishonesty can lead to disciplinary
action.”
All students sitting for this examination are required to rearm the above-
mentioned honesty pledge by writing the below statement with your
signature and date onto the first exam answer sheet. Students who
fail to do so may lead to severe penalties, including the receipt of a zero mark
in the examination.
“I, [Student Name (SID)], pledge to follow the Rules on Academic
Honesty and understand that violations may lead to severe penalties.”
Signature
Date
2
Page 1 of 4

PART 1: MULTIPLE CHOICE QUESTIONS (5 POINTS EACH)

Question 1: What are different types of economic data?

A. Time series
B. Cross sectional
C. Observational
D. Both A and B
E. Both A and C

Question 2: Weak stationarity is also called

A. Strong stationarity
B. Distribution stationarity
C. Covariance stationary
D. Mean stationary
E. Mean stationarity

Question 3: How are autocovariance and autocorrelation related?

A. Autocovariance is autocorrelation divided by the variance
B. Autocovariance is autocorrelation multiplied by the standard deviation
C. Autocorrelation is autocovariance divided by the variance
D. Autocorrelation is autocovariance multiplied by the standard deviation
E. Autocorrelation is autocovariance divided by the standard deviation

Question 4: If you want to do exploratory data analysis on univariate time series data, which of the
following would you not do?

A. Bar plot
B. Normality test
C. Histogram
D. Time series plot
E. Scatterplot


Question 5: If you see a return series 35%, -20%, 10%, 40%, and -25%, what are the arithmetic and
geometric means?

A. 8% and 4.5%
B. 7% and 4%
C. 7% and 4.5%
D. 8% and 4%
E. 4% and 8%


Question 6: Adjusted R-squared is
Page 2 of 4


A. Higher than the unadjusted R-square
B. Lower than the unadjusted R-square
C. Accounts for the number of regressors
D. A and C
E. B and C


Question 7: The objective function of ordinary least squares minimizes sum of squared errors. This is also
called

A. Mean absolute loss
B. Mean quadratic loss
C. Quadratic loss
D. Absolute loss
E. Asymmetric loss


Question 8: We need to model trend in a series because a deterministic trend

A. Influences the stationarity of the series
B. Is correlated with regression errors
C. Adds to multicollinearity
D. Makes the data difficult to model
E. B and C


Question 9: What is seasonality?

A. Period changes to a data series that are unpredictable
B. Period changes to a data series that are predictable
C. Aperiodic, unpredictable changes to a data series
D. Aperiodic, predictable changes to a data series
E. Unpredictable changes to a data series


Question 10: What are the ACF and PACF of a white noise process at the second lag?

A. (0.5, 0)
B. (0, 0.5)
C. (0.5, 0.5)
D. (0, 0)
E. (0, 1)


Page 3 of 4


PART 2: SHORT ANSWER QUESTIONS


Question 11: You model the trend of a series in three ways: linear, quadratic, and exponential. You get
the following table for Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC).
Which model do you pick and why? (6 points)




Question 12: Explain the notion of autocorrelation function and partial autocorrelation function. Is it
possible autocorrelations at certain displacements be positive while the partial autocorrelation be negative?
Why or why not? (10 points)


Question 13: You land an interview at a prestigious investment bank. Your interviewer is intrigued that
you have taken a course on financial data science and forecasting. She decides to test your knowledge of
the autocovariance structure of covariance stationary series and lists the following autocovariance
functions. Explain which ones are consistent with covariance stationarity, which are not, and why? (8
points each)

a) ߛሺݐǡ ߬ሻ ൌ ߙ for a constant ߙ ് Ͳ

b) ߛሺݐǡ ߬ሻ ൌ ݁ିఈఛ

c) ߛሺݐǡ ߬ሻ ൌ ఈ
௧




Question 14: Rewrite the following expressions without using the lag operator, in the form of ݕ௧ ൌ ڮ (6
points each)

a) ܮହݕ௧ ൌ ߳௧

b) ݕ௧ ൌ ʹ ቀͳ ൅
௅య
௅
ቁ ߳௧

c) ݕ௧ ൌ
ଵାସ௅ା଴Ǥ଻௅మ
௅ି଴Ǥସ௅య
߳௧
Page 4 of 4



Question 15: Rewrite the following expressions using the lag operator. (6 points each)

a) ݕ௧ ൅ ݕ௧ିଵ ൅ڮ൅ ݕ௧ିே ൌ ߙ ൅ ߳௧ ൅ ߳௧ିଵ ൅ ڮ൅߳௧ିே

b) ݕ௧ ൅ ݕ௧ିఛ ൌ ߳௧ିଶ ൅ ߳௧ିଵ ൅ ߳௧


Question 16: Suppose we have an AR(1) process ݕ௧ ൌ ߶ݕ௧ିଵ ൅ ߳௧

a) What is the one-step-ahead forecast ݕ்ାଵǡ்? What is the forecast error? (5 points)

b) What is the two-step-ahead forecast ݕ்ାଶǡ்? What is the forecast error? (7 points)

c) What is the h-step-ahead forecast ݕ்ା௛ǡ்? What is the forecast error? (7 points)