Time Series Exam Project

This Github repository contains the Time Series project for the Time Series course supervised by Florian Ielpo. This is a project based on the analysis of the "data_exam.xlsx" spreadsheet. The goal is to demonstrate that we can convert daily returns to intra-day returns using the Parkinson volatility indicator, by studying the joint relationships of the time series.

Data Description

The "data_exam.xlsx" spreadsheet contains three columns:

• Column B: VIX level, which measures the volatility of the S&P 500 index.
• Column C: Parkinson estimates, which is a measure of volatility based on high, low, and closing prices.
• Column D: Squared returns, which is a measure of variance based on daily returns squared.

Questions to Answer

The following questions will be answered in this project:

1. Explain the concept behind each column. What are these time series meant to represent? Transform these time series so that they are comparable in scale and order.
2. Estimate an AR model on each of these time series. Determine the order of the AR process and show the estimates. What can you conclude from these estimations?
3. Plot the fitted values for each model vs. the original time series. Why are these fitted values appealing for volatility measuring purposes?
4. Estimate an HAR model on each time series. Present the estimated coefficients of the model and compare the loglikelihood of each model to the one obtained from the AR estimations. Which model do you prefer? Retain the fitted values of the model you have selected for each of the three time series.
5. Test for the stationarity of the estimated time series. Comment on the results.
6. Estimate a VAR(p) model on your three stationary fitted values. Comment on the results.
7. Plot an impulse response function obtained from your VAR model and comment on the results.

Repository Contents

• reportings/data_exam.xlsx: The Excel spreadsheet containing the data to be analyzed.
• reportings/notebook.ipynb: A Jupyter notebook containing the code for the analysis and answers to the questions.
• Exam.pdf: The Exam pdf provided by F.Ielpo
• notes_cours_TimeSeries.pdf: Some of our notes.

Contributors :

• Sarra Ben Yahia
• José Ángel García Sánchez