Spring 2025 Term 1 Project - Discrete Fourier Transform Using Bike Share Data

Project Details:

This class is focused on the fundamentals of time series analysis: exploration and modelling using ARIMA and state-space techniques. These methods form the basis for countless more complicated and/ or specialized methods.

In practice, the methods you use will depend on your data and your research question. Your task for the final project is to research a method for time series data that is not thoroughly covered in this class (but that builds on methods that are covered). The following are your options for techniques to focus on:

• X11 decomposition (a more sophisticated decomposition as compared with Lab 1 assignment)
• Analyzing seasonality/ cycles using the Discrete Fourier Transform
• TGARCH (Threshold GARCH) models for modelling the variance of a time series. We will discuss GARCH models in class after the midterm. TGARCH is an extension of this model type.
• Stochastic volatility models (using the state-space framework). We will cover this in class after the midterm, but it warrants further exploration!
• VAR(p) models (vector autoregression)
• Other

The primary deliverable consists of a paper (with supporting code) and a presentation (15 minutes). Your paper must include the following sections, at a minimum:

1. Introduction: Brief description of the method, the data, and why this method is appropriate for your dataset
2. Method: Describe the method in detail, with appropriate citations. Include a toy example that displays the use of the method on a very simple (probably simulated) dataset.
3. Application: Use the method on the dataset of your choice. Provide detail on your dataset using exploratory techniques (plots, tables). Describe the results in detail, using plots where appropriate.
4. Conclusion: What were the strengths and weaknesses of the method for your dataset. What insights about your data were gleaned from this analysis.