Topic: Estimation and Forecasting tasks.

CW-STAT 1050.Instructions are in the attached file. Ask a question for clarifications.Restrictions: A maximum of 4 pages (and no more will be accepted)

Topic: Estimation and Forecasting tasks.

Data: Yahoo finance using R package quantmod to get your data

Report: Use headings to identify each section in your report. Necessary graphs and tables must be copied from your spreadsheet into the Report (always use “Paste as Picture” to avoid linking). Do NOT copy any time series list into your report e.g. dates and prices. State the mathematical definitions of any quantities that you describe.

Expectations: Your report should satisfy the following aspects – Writing style: Critical report (Scope of analysis and tests conducted; mathematical equations were appliable should be given and explain) – Depth: Critical analysis of results (Tests should be explained in detail covering the mathematical aspects, analysis of test assumptions and explanations/implications of results to the whole study and not targeting to only translate the output of each test. R coding: You can find some nice examples on the links below: You will need the following libraries installed: library(stats) library(quantmod) library(forecast)

DOES you paper meet these requirements? of course no, so make it a good paper. Let me hear from you.

Coursework tasks

Using the package quantmod download S&P500 index price data covering the period (yyyy/mm/dd) 2009/01/01 to 2023/10/31. Use daily data.

For each of your answers below you will need to:

• Show the 1-liner code responsible for the output
• Write the respective mathematical equation i.e., for log-returns and/or for the ARIMA model fit
• Explain any hypothesis testing: (i) What is the underlying hypothesis test null and alternative hypothesis, (ii) comment on the p-values
• Display plots, with caption and explanation
• No screenshots of results are allowed

STAT1050 (2023/24)
Statistical Methods
Contribution: 100% of
for Time Series
course
Course Leader:
Time Series Analysis Deadline Date:
Dr Konstantinos Skindilias
Coursework
Wednesday 6th DEC 2023
This coursework will be marked anonymously
YOU MUST NOT PUT ANY INDICATION OF YOUR IDENTITY IN YOUR
SUBMISSION
This coursework should take an average student who is up-to-date with tutorial work
approximately 15 hours
Feedback and grades are normally made available within 15 working days of the
coursework deadline
Learning Outcomes:
1. Critically evaluate the generated model output and underlying model assumptions
together with their implications of respective advanced modelling and statistical
techniques for time series analysis.
2. Demonstrate critical awareness by making a result driven choice of the most
appropriate statistical tools to analyse time series data, model fitting/ estimation, and
forecasting. Apply different linear regression models to time series data, select
challenger models and critically assess when to use Machine Learning libraries.
3. Demonstrate a comprehensive understanding in autoregressive (AR) and moving
average (MA) processes, their coupling as ARIMA integrated processes by applying
them to a range of time series data using a suitable statistical package and where
applicable Machine Learning techniques. Critically evaluate and interpret program
output and be able to conduct a critical report for discussing the results and
implications of the study.
Plagiarism is presenting somebody else’s work as your own. It
includes copying information directly from the Web or books without
referencing the material; submitting joint coursework as an individual
effort; copying another student’s coursework; stealing coursework
from another student and submitting it as your own work. Suspected
plagiarism will be investigated and if found to have occurred will be
dealt with according to the procedures set down by the University.
Please see your student handbook for further details of what is / isn’t
plagiarism.
All material copied or amended from any source (e.g. internet, books) must
be referenced correctly according to the reference style you are using.
Your work will be submitted for plagiarism checking. Any attempt to bypass
our plagiarism detection systems will be treated as a severe Assessment
Offence.
Coursework Submission Requirements
•
•
•
•
•
•
•
An electronic copy of your work for this coursework must be fully
uploaded on the Deadline Date of Wednesday 6th DEC 2023 using the link
on the coursework Moodle page for STAT1050.
For this coursework you must submit a single PDF document. In
general, any text in the document must not be an image (i.e. must not be
scanned) and would normally be generated from other documents (e.g.
MS Office using “Save As .. PDF”). An exception to this is handwritten
mathematical notation, but when scanning does ensure the file size is
not excessive.
There are limits on the file size (see the relevant course Moodle page).
Make sure that any files you upload are virus-free and not protected by a
password or corrupted otherwise they will be treated as null
submissions.
Your work will not be printed in colour. Please ensure that any pages
with colour are acceptable when printed in Black and White.
You must NOT submit a paper copy of this coursework.
All coursework must be submitted as above. Under no circumstances
can they be accepted by academic staff
The University website has details of the current Coursework Regulations,
including details of penalties for late submission, procedures for
Extenuating Circumstances, and penalties for Assessment
Offences. See http://www2.gre.ac.uk/current-students/regs
•
•
•
•
0-30
31-39
40-49
50-59
Detailed Specification
Coursework must be completed individually. Students are
allowed to work in groups in order to produce results and
discuss implications of their findings
Deliverables
Single PDF document. No Excel file should be uploaded and R
output.
Grading Criteria
Marks will be distributed as follows:
An unsatisfactory submission that demonstrates little understanding of the subject matter.
A substandard submission which has no critical appraisal of the numerical methods and
concepts of scientific methodology.
A satisfactory submission with a basic understanding of the models used and basic descriptions
with no proofs
A submission which includes a reasonable understanding of the underlying models, has some
proofs and basic discussion.
60-69
70+
80+
A good submission which includes a good understanding of the numerical methods and
concepts of scientific algorithms. Elaboration and discussion of the underlying theory,
implications of tests, results and underlying models.
A very good submission that clearly demonstrates the relative merits of the underlying models
and implications of their use. Detailed discussion of the results, underlying theory and relating
the dynamics of the underlying time series to those implied by the models. Equations and
proofs are given where necessary with critical derivation and discussion.
An excellent submission which demonstrates a clear understanding of the underlying models
and implications of their use. Clear derivation and presentation of all necessary formulas used
and implications of their dynamics relevant to the dynamics of the time series under
investigation. Excellent discussion of the underlying theory of discrete time stochastic
processes, methodology and theory of financial markets.
STAT-1050 Statistical Methods for Time Series
Deadline: Wednesday 6th DEC 2023. Please upload your report before 21:30pm.
Submission: online via Moodle.
Deliverables – PDF Processed Analysis Report incorporating R outputs where necessary,
such as tables, plots, etc.
In detail:
– Do not upload the R file
– Do not upload direct copies of R or code chunks – convert to table/ plot
– No handwritten notes should be attached on the report.
– You should use Microsoft Equation editor (or the built-in equation editor).
– You will need to find the best way of displaying your results (Tables, Plots)
using the PAGE restriction in place
– No scanned/image output (will end up in subtracting marks)
– Your final report to be uploaded must be converted into a PDF
What you are expected of: Show all underlying theory behind every computation you make,
derive all equations, and explain in detail all formulas, background theory and implications
of each theoretical assumption.
Restrictions:
A maximum of 4 pages (and no more will be accepted)
Topic:
Estimation and Forecasting tasks.
Data:
Yahoo finance using R package quantmod to get your data
Report:
Use headings to identify each section in your report. Necessary graphs and tables must be
copied from your spreadsheet into the Report (always use “Paste as Picture” to avoid
linking). Do NOT copy any time series list into your report e.g. dates and prices. State the
mathematical definitions of any quantities that you describe.
Expectations:
Your report should satisfy the following aspects
– Writing style: Critical report (Scope of analysis and tests conducted; mathematical
equations were appliable should be given and explain)
– Depth: Critical analysis of results (Tests should be explained in detail covering the
mathematical aspects, analysis of test assumptions and explanations/implications
of results to the whole study and not targeting to only translate the output of each
test.
R coding:
You can find some nice examples on the links below:
You will need the following libraries installed:
library(stats)
library(quantmod)
library(forecast)
Excel Spreadsheet:
No Excel spreadsheet should be submitted. Your report should contain all necessary
information for a complete understanding of your analysis.
Mark Weighting:
See within.
Assessment: You must provide evidence of understanding. This implies that you are
required to discuss the relevant theory behind any of your calculations and implementation.
To achieve full marks, you will need to devise the appropriate amount of discussion behind
the theory and formulas used and methodology as applied to the relevant time series data.
ALL EQUATIONS SHOULD BE GIVEN AND DISCUSSION AT AN APPROPRIATE LEVEL MUST BE
GIVEN.
Coursework tasks
Using the package quantmod download S&P500 index price data covering the period
(yyyy/mm/dd) 2009/01/01 to 2023/10/31. Use daily data.
For each of your answers below you will need to:
– Show the 1-liner code responsible for the output
– Write the respective mathematical equation i.e., for log-returns and/or for the
ARIMA model fit
– Explain any hypothesis testing: (i) What is the underlying hypothesis test null and
alternative hypothesis, (ii) comment on the p-values
– Display plots, with caption and explanation
– No screenshots of results are allowed
[Total: 100 marks]
On the series:
(i)
Obtain the time series using the correction code syntax making use of the code
below
library(quantmod)
# Obj 1: Load stock prices by symbol
getSymbols(symbol)
(ii)
Transform your series to log-returns
[5 marks]
[5 marks]
(iii)
Examine the ACF and PACF functions
(iv)
Perform the Ljung-Box test and describe the test-hypothesis and
report/comment on the result.
[10 marks]
[10 marks]
(v)
Check the data for stationarity using the correct test statistic and comment on
the output
[10 marks]
(vi)
Perform a normality test of your choice on the return series and report the
output.
Write down the hypothesis test and comment on the p-value
[10 marks]
(vii)
Fit an ARIMA model and determine the correct lag order: Show the 1-liner codes
for output.
[15 marks]
(viii)
Report the coefficients for the chosen ARIMA model and show the respective
equation given these coefficients
[15 marks]
(ix)
The residuals from an ARIMA fit require that:
a. The residuals have zero mean 𝐸 [𝑒! ] = 0
b. Have a finite variance 𝑉𝑎𝑟 [𝑒! ] = 𝜎 ”
c. Have zero autocovariance 𝐸 [𝑒! 𝑒# ] = 0
Using the results from checkresiduals(fitted_model) function comment on the above
[20 marks]