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 [email protected], [email protected], [email protected] 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) for a constant b) c) Question 14: Rewrite the following expressions without using the lag operator, in the form of (6 points each) a) b) c) Page 4 of 4 Question 15: Rewrite the following expressions using the lag operator. (6 points each) a) b) Question 16: Suppose we have an AR(1) process a) What is the one-step-ahead forecast What is the forecast error (5 points) b) What is the two-step-ahead forecast What is the forecast error (7 points) c) What is the h-step-ahead forecast What is the forecast error (7 points)