DSM120 Time Series Forecasting Assignment : Financial Data Analysis Case Study Using AR Models & Monte Carlo Simulation

Background

The coursework is designed to directly support the learning outcomes of the module by providing you with a hands-on approach to analysing real-world time-based data, particularly in financial contexts.

Through the portfolio-based assessment, you will apply key time series analysis techniques. A major focus of the coursework is on predicting future values of time series, requiring you to engage with regression models, Monte Carlo simulations, and autoregressive methods. In addition, the open-ended component of the coursework aligns with the module’s broader objective of equipping you with the ability to independently investigate, analyse, and make predictions on complex time- based data using both traditional and modern computational techniques.

The coursework assignment

Part 1

At the end of each of the first five topics, you will find a section outlining what you should include in your portfolio at that stage. Your submission should provide a structured account of your engagement with each topic, demonstrating both implementation and critical analysis. This should include:

• A summary of your approach, describing the steps you have taken and the
  reasoning behind your choices.
• Results presented clearly, using graphs, error estimates, or any other
  appropriate method to communicate findings effectively.
• The software and code used, ensuring reproducibility and clarity in
  implementation.
• A reflection on your findings, discussing observations about the datasets and
  methods explored.
• A critical evaluation of the models applied, assessing their limitations, and the
  insights gained from your analysis.

[60 marks]

Part 2

In this section, you will extend your analysis by conducting ACF, PACF, and AR(q) predictions at two different frequencies of the selected high-frequency dataset. For example, you may extract data at intervals of 5 minutes and 10 minutes and perform comparative analysis.

Use Monte Carlo methods in conjunction with AR(q) to simulate 25 potential future scenarios for each frequency for both 5-minute and 10-minute data intervals. Employ kernel density estimation (KDE) to estimate the probability distributions of these future scenarios, providing insights into forecast uncertainty.

Compare and evaluate forecasting performance across both frequencies,
considering model effectiveness at different time resolutions. Explore how alternative forecasting approaches, parameter refinements, or extended comparisons can provide deeper insights.

[20 marks]

Part 3

The last part of the coursework is more open-ended. You should extend your
analysis by both applying familiar techniques in a new way and exploring an
approach that we have not covered in detail during the lectures. To achieve full
marks, you should engage in both aspects of this exploration.

You may wish to consider that the topics that we think will be covered are STL
decomposition, ARIMA, Vector Auto Regression, ARCH, GARCH, and Kalman filter.
Some possibilities for things not covered are deep learning, recurrent neural
networks, and technical trading analyses.

[20 marks]

How this coursework will be graded

The marks in this coursework are allocated as follows:

Part 1

There are 60 marks available for completing tasks outlined at the bottom of each of the first five topics. You do not need to perform any additional implementation, and it is perfectly acceptable to use stats models or other libraries. For each of those five topics:

• Up to 4 marks for producing the results of the main algorithms on selected
  data. Full marks will be awarded for well-structured implementation with
  appropriate visualisation.
• Up to 4 marks for reflecting on how well the method works under different
  conditions, with clear discussion of its strengths and limitations.
• Up to 4 marks for exploring beyond the standard implementation, such as
  comparing multiple approaches, experimenting with different parameters, or
  applying additional evaluation metrics.

Part 2

There are 20 marks available for completing this part:

• Up to 8 marks for conducting ACF, PACF, and AR(q) analysis at two different
  frequencies, demonstrating correct implementation and a well-reasoned
  discussion of the results.
• Up to 8 marks for applying Monte Carlo methods in conjunction with AR(q),
  ensuring well-structured simulations, appropriate visualisations, and insightful
  interpretation, including Kernel Density Estimation (KDE) to assess probability
  distributions of future scenarios.
• Up to 4 marks for extending the analysis beyond standard implementation,
  such as comparing different forecasting approaches, evaluating performance
  variations across time resolutions, or refining parameter selection.

Part 3

The remaining 20 marks are more open-ended, and more attuned to your creativity and backgrounds. There are several ways to obtain these marks, and it is up to you to put them together.

• Up to 10 marks for finding something different and conducting the kind of
  analysis we have been doing in the topics. You can do two of these.
• Up to 10 marks for investigating an approach that was not covered in detail in
  the lectures. Your submission should include both implementation and an
  evaluation of its results.

References

Alongside the course materials, for essential reading on time series forecasting and
analysis, please refer to:

• Rob J. Hyndman & George Athanasopoulos (2021), Forecasting: Principles
  and Practice (Online Book) – A widely used, frequently updated resource
  covering key forecasting concepts.
• Franses, van Dijk, & Opschoor, Time Series Models for Business and
  Economic Forecasting – Focuses on the role of time series in economic
  modeling.
• James Douglas Hamilton (1994), Time Series Analysis – A comprehensive,
  mathematically rigorous reference for advanced time series methods.

A full list of reading materials is available on the VLE page.