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BUSN 5002 Fundamentals of Business Analytics
发布时间：2022-11-03
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BUSN 5002 Fundamentals of Business Analytics
Final Exam Preliminaries - Fundamentals of Business Analytics - ECON5002, Semester I 2022
The final exam will be online on June 8th , starting at 9:00 AM and finishing at 11:00 AM (2 hours including reading time). The exam will be available on LMS. The exam is written in a editable pdf file. The final exam comprises of two questions. Below are the instructions of the final exam front page
INSTRUCTIONS:
1. Total number of points: 100 points.
2. Type your answer only in the provided space.
3. After finishing the exam, submit this file with your answers by 11:00 am using the dedicated LMS link. Label the file as [Name Initials] FE.pdf.
4. Submit one computer code for each question by 11:30 am using the dedicated LMS link. Label the files as [Name Initials] q1.r and [Name Initials] q2.r for questions 1 and 2 respectively. I should be able to run your script file and reproduce the results reported in the exam.
Prepare your R script codes based on the following guidelines.
Question 1 The data capm .csv have observations from daily rates of return comprising the period
of January 2007 to December 2013. The variables are described below:
|
data |
capm .csv |
|
|
Date Mkt.RF SMB HML RF GE CISCO DD XOM |
day/month/year Market minus Risk free return Return of companies with low market capitalization Return of companies with high book-to-market values Risk Free return General Electric CISCO DuPont Exxon-Mobil |
|
Let us explore again the CAPM model. The regression models to be investigated could be
r[?] − rrf = α + β × (rmkt − rrf ) + u
r[?] − rrf = α + β × (rmkt − rrf ) + γ × smb + u
r[?] − rrf = α + β × (rmkt − rrf ) + δ × hml + u
r[?] − rrf = α + β × (rmkt − rrf ) + γ × smb + δ × hml + u.
where r[?] is the return of one asset to be informed on the exam paper (GE, CISCO, DD or XOM), rrf is the risk free return, rmkt is the market return, and smb and hml correspond to SMB and HTM defined in the above Table. The variable u is the error term. You should be able to:
(a) Subset the data. For example, I can ask you to use data from December 2009 to January 2012. I can also ask you to use data from two subperiods.
(b) Produce a scatter plot with (r[?] − rrf ) on the y- axis and (rmkt − rrf ) on the x- axis, and include the regression line in it.
(c) Estimate α , β , γ, and δ and their respective standard errors. Consider that the errors might be heteroskedastic. Verify if the estimated coefficients are statistically significant. Interpret the coefficients of the regressions.
(d) Estimate confidence intervals for α , β , γ, and δ possibly assuming heteroskedas- ticity of the variance of the residuals.
(e) Perform hypothesis testing on the parameters of the model (single or joint rescric- tions) possibly assuming heteroskedasticity of the variance of the errors.
(f) Test if the errors are heteroskedastic (Breustch-Pagan test), and interpret the result.
(g) Perform model comparison tests, considering that one or more models are nested into a large model (waldtest).
Question 2 We now study the univariate time series sequence avaiable at the time series .csv file. This series contains 600 observations. Let us call this series yt which can follow an ARMA(p,q) process
yt = µ + ϕ1yt −1 + ... + ϕpyt −p + υt + ψ1 υt −1 + ... + ψq υt −q
The lags of the autoregressive and moving average components will be informed on the exam paper. You should be able to:
(a) Plot the series across time.
(b) Plot the autocorrelation and partial autocorrelation functions (ACF and PACF, respectively), and use this information to determine the order of the ARMA.
(c) Estimate µ , ϕ\ s, and ψ \ s, and their respective standard errors. Verify if the estimated coefficients are statistically significant.
(d) Perform diagnostic tests (Ljung-Box) on the residuals.
(e) Perform model comparison (AIC and BIC).
