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QBUS2810 Statistical Modelling for Business

创建日期：2024-04-29 17:02:03

所属分类：数学mathematics

标签： QBUS2810

Statistical Modelling for Business

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QBUS2810

Statistical Modelling for Business
Individual Assignment
This assignment is worth 20% of your final mark in the unit.
The deadline is Monday, March 28th by 11:59pm Sydney time.
Submission is via TurnItIn on Canvas.
Requirements:
• Complete your entire assignment in Jupyter Notebook, including your code and
markdown sections for your written answers. Use Latex in markdown sections
where needed.
• Submit the resulting downloaded html file as your entire assignment. Care must
be taken with presentation in this file, however unavoidable error messages and
page formatting issues will be ignored in marking.
• Only relevant analysis outputs (graphs, tables, etc) should appear in the as-
signment file and all output should appear together with the discussion of that
output, in the file.
Task 1 (30 marks). Business problem:
This assignment follows the analysis conducted in the lectures regarding the dependence
between earnings and asset returns for companies listed on the NYSE. You will assess
whether earnings in one year (say t−1) affect asset returns in the subsequent year (say
t), and in particular whether returns are typically higher following positive, compared
to negative, earnings years and also assess whether there may be a linear relationship
between returns and lagged earnings.
Data: The data file for the analysis is “SampleData from US 90 08 wk3.csv” which
was sampled from “US 90 08 wk3.csv”.
2Questions:
(a) Conduct an appropriate exploratory analysis on the asset returns, both individually
and in terms of one of the primary questions being considered in this assignment:
are returns in the subsequent year t typically higher following positive, compared to
negative, earnings years in year t − 1? Discuss any cleaning of the data you did,
including why and how you did it, or why you did not do it. (3 marks)
(b) Conduct the appropriate t-test (with α = 0.05), median and Mann-Whitney tests,
to assess whether returns are typically higher following positive, compared to negative,
earnings years. For median tests, use two-sided testing. Assess all assumptions made.
(10 marks)
(c) Which test’s result do you believe the most in part (b)? Discuss and explain. (2
marks)
(d) Conduct an appropriate exploratory analysis to assess whether there may be a
linear relationship between returns and lagged earnings. (3 marks)
(e) Conduct a simple linear regression analysis, using OLS estimation, for returns on
lagged earnings. Fully assess all assumptions of OLS. Also obtain the LAD estimates
and list and assess the assumptions of LAD. Discuss any cleaning of the data you did,
including why and how you did it, or why you didn’t do it. (9 marks)
(f) Write a brief (< 0.5 page) report summarising and discussing your findings and
conclusions in layman’s terms. Include a discussion of whether you would recommend
an investment strategy based on your findings. (3 marks)
Task 2 (20 marks). Theoretical derivations:
Consider the population SLR model:
Yi = β0 + β1Xi + εi
and an observed, random sample of data (y1, x1), . . . , (yn, xn) from that model. An
OLS regression is run on this data.
3Questions:
(a) Show that under LSA 1, the OLS slope estimator can be written as βˆ1 = β1 +∑n
i=1 aiεi, where ai =
xi−x¯∑n
i=1(xi−x¯)2 . Hint: take the formula for βˆ1 from slide 13 of Lecture
4, write it in terms of yi and ai and then plug in the formula for yi under LSA 1. (3
marks)
(b) Show that under LSA 3 and 5 the variance of the OLS estimator of β1 can be
written as V (βˆ1|x) = σ2
∑n
i=1 a
2
i . Where did you use each assumption? Hint: use
result in part (a) to write out the variance in a general form and see what simplifies
and why. (5 marks)
(c) Show that the formula in par (b) can be equivalenly written as V (βˆ1|x) = σ2∑n
i=1(xi−x¯)2
(3 marks)
(d) Show that if LSA 5 is relaxed (but LSA 3 is maintained) the variance formula
can be written as V (βˆ1|x) =
∑n
i=1 a
2
iV (εi|xi) . Argue why
∑n
i=1 a
2
i e
2
i is a reasonable
estimator of V (βˆ1|x) in this case. (4 marks)
(e) Suppose you had estimates of covariances ˆcov(εi, εj) and propose a reasonable
estimator of V (βˆ1|x) if both LSA 3 and 5 are relaxed. How would you estimate the
component that depends on ˆcov(εi, εj)? (5 marks)

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CS 333 CP1406 KIT308 Economics 701 ECON3740 ECE 5759 BFC3340 FINC2012 COMP4500 MATH3871 FIT3080 18-819C Economic ECO202Y5Y PHY100 FINC-780 Econ 100B EC602 IE582 EE450 COMP9517 WRDS 150B ECON 570 LECTURE 2 ECA5101 ECE 4420 ADAD9311 FIT3031 CS 544 MF 703 CS 6140 KIT501 ENGSCI 344 CSC171 IE 332 FINM8007 21S2 COSC 1114 FE545 E471 SIT102 CSC108 MAT301 IAE 101 COP3503 STAT2004 EC 303 CS1026 STAT1203 MATH3171 ISOM5160 IFN657 FIT2014 ACCT2102 DSCI550 STATS 330 ELEC421 COMP3670 QBUS6840 MEES:698B MAST30027 MIET1077 Economics IFT 6758 FIT5122 BUSN5101 CptS 111 HRMT5502 Math2018 PP 312 INFS3200 CZ3005 CSSE1001 SENG 2011 MKTG 553Q BUFN 640 COMP507 ETF5952 DATA 311 ECE4043 BANK3011 finance M3H623544 HW1 INFS 7410 AI6103 STAT3888 INFS3208 ACCT7103 ECOS3013 PSYCH 20B F79MA STAT3006 ENGG952 2X MGSC 7000 ECE4132 MSF 526 MATH 3033 CDS 511 EEEE4120 EEET2465 ECA5103 MATH2070 ELEC3104 BU51019 EEE8147 ENGR20003 COSC 1107 ETF3200 FNCE 435 MSFI 435 ISyE6420 GENG4405 HW ETC5523 IE 7315 MOEC0021 STA 106 ENGG 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