BUSS6002代做、代写Python语言编程

日期：2025-05-27 09:03

BUSS6002 Assignment

Semester 1, 2025

Instructions

• Due: at 23:59 on Friday, May 23, 2025 (end of week 12).

• You must submit a written report (in PDF) with the following filename format, replacing

STUDENTID with your own student ID: BUSS6002 STUDENTID.pdf.

• You must also submit a Jupyter Notebook (.ipynb) file with the following filename format,

replacing STUDENTID with your own student ID: BUSS6002 STUDENTID.ipynb.

• There is a limit of 6 A4-pages for your report (including equations, tables, and captions).

• Your report should have an appropriate title (of your own choice).

• Do not include a cover page.

• All plots, computational tasks, and results must be completed using Python.

• Each section of your report must be clearly labelled with a heading.

• Do not include any Python code as part of your report.

• All figures must be appropriately sized and have readable axis labels and legends (where

applicable).

• The submitted .ipynb file must contain all the code used in the development of your report.

• The submitted .ipynb file must be free of any errors, and the results must be reproducible.

• You may submit multiple times but only your last submission will be marked.

• A late penalty applies if you submit your assignment late without a successful special con sideration (or simple extension). See the Unit Outline for more details.

• Generative AI tools (such as ChatGPT) may be used for this assignment but you must add a

statement at the end of your report specifying how generative AI was used. E.g., Generative

AI was used only used for editing the final report text.

• Hint! It is highly recommended that you finish the week 10 tutorial before starting this

assignment.

1

Description

The VIX Index, often called the “fear gauge”, measures the market’s expectations of near-term

volatility based on S&P 500 option prices. Predicting the VIX index is useful because it helps

investors anticipate market volatility and manage risk more effectively in their investment strate gies. In this assignment, you are conducting a study that compares the predictive performance

between four families of basis functions: piece-wise constant, piece-wise linear, radial, and Laplace,

for a linear basis function (LBF) model designed to predict the VIX index value. The aim is to

investigate which family of basis functions is most suited for modelling the relationship between

time and volatility (measured by VIX).

You are provided with the VIX dataset, which is widely used in financial market research. The

dataset contains 8,920 observations of daily VIX values (vix) from 1990 to 2025. It also contains

the year (year) for which the value is observed. A scatter plot of the dataset is shown in Figure 1.

Figure 1: VIX levels from 1990 to 2025.

The specific LBF model being considered in your study is given by

y = ϕ(x)

⊤β + ε,

where y is the VIX value, x is year, and ε is a random noise; ϕ(x) denotes the vector of basis

function values; the parameter vector to be estimated is β. Four families of basis functions are

considered for computing ϕ(x); the first family is the set of piece-wise constant basis functions

ϕ(x) := [1, γ1(x), . . . , γk(x)]⊤, with

γi(x) := I(x > ti),

where I(x > ti) is an indicator function defined by

I(x > ti) := ( 1 if x > ti

0 if x ≤ ti

.

The break points {ti}

k

i=1 are calculated according to

ti

:= xmin +

i(xmax − xmin)

k + 1

, (1)

2

where xmin and xmax denote the smallest and largest observed values of x, respectively. The second

family is the set of piece-wise linear basis functions ϕ(x) := [1, x, λ1(x), . . . , λk(x)]⊤, with

λi(x) := (x − ti)I(x > ti),

where ti

is given by Equation (1). The third family is the set of radial basis functions ϕ(x) :=

[1, ρ1(x), . . . , ρk(x)]⊤, with

ρi(x) := exp  −

(x −

8

ti)

2

,

where ti

is given by Equation (1). The final family is the set of Laplace basis functions ϕ(x) :=

[1, τ1(x), . . . , τk(x)]⊤, with

τi(x) := exp  −

|x −

8

ti

|



,

where ti

is given by Equation (1).

Before comparing the four basis function families, you must set the number of components k

for all models. This hyperparameter value for each basis function family should be selected using

a validation set, by minimising the validation mean squared error (MSE).

You should select the optimal values of k by exhaustively searching through an equally-spaced

grid from 1 to 30, with a spacing of 1:

K := {1, 2, . . . , 30}.

Once the optimal values of the hyperparameters are chosen for all basis function families, you will

be able to compare the predictive performance between the four using a test set (i.e., by comparing

the test MSE between the four optimally selected models).

3

Report Structure

Your report must contain the following four sections:

Report Title

1 Introduction (0.5 pages)

– Provide a brief project background so that the reader of your report can understand

the general problem that you are solving.

– Motivate your research question.

– State the aim of your project.

– Provide a short summary of each of the rest of the sections in your report (e.g., “The

report proceeds as follows: Section 2 presents . . . ”).

2 Methodology (2 pages)

– Define and describe the LBF model.

– Define and describe the four choices of basis function families being investigated.

– Describe how the parameter vector β is estimated given the value of the hyperparameter

k. Discuss any potential numerical issues associated with the estimation procedure.

– Describe how the hyperparameter value can be determined automatically from data (as

opposed to manually setting the hyperparameter to an arbitrary value).

– Describe how the performance of the four families of basis functions is compared given

the optimal hyperparameter value.

3 Empirical Study (2.5 pages)

– Describe the datasets used in your study.

– Present (in a table) the selected hyperparameter value for each basis function family.

– Describe and discuss the table of selected hyperparameters.

– Visually present (using plots) the predicted response values for each basis function

family in the test set.

– Describe and discuss the plots of predicted values.

– Present (in a table) the test MSE values for each basis function family.

– Describe and discuss the table of test MSE values.

– Report the VIX forecasts of 2026, 2027, and 2028, given by the model with the smallest

test MSE. Include a brief description of how these forecasts are obtained.

4 Conclusion (0.5 pages)

– Discuss your overall findings / insights.

– Discuss any limitations of your study.

– Suggest potential directions of extending your study.

4

Rubric

This assignment is worth 30% of the unit’s marks. The assessment is designed to test your compu tational skills in implementing algorithms and conducting empirical experiments, as well as your

communication skills in writing a concise and coherent report presenting your approach and results.

The mark allocation across assessment items is given in Table 1.

Assessment Item Goal Marks

Section 1 Introduction 4

Section 2 Methodology 10

Section 3 Empirical Study 16

Section 4 Conclusion 3

Overall Presentation Clear, concise, coherent, and correct 5

Jupyter Notebook Reproducable results 2

Total 40

Table 1: Assessment Items and Mark Allocation

5