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https://github.com/ibaris/finance-tda

Topological Tail Dependence: Evidence from Forecasting Realized Volatility
https://github.com/ibaris/finance-tda

finance quant risk-analysis topological-data-analysis volatility-modeling

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Topological Tail Dependence: Evidence from Forecasting Realized Volatility

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Finance TDA

Topological Tail Dependence: Evidence from Forecasting Realized Volatility


[v-2024.2.3]



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  Introduction •

  Installation •

  Documentation •

  Example •

  Reference






# Introduction



This repository hosts the Python package developed from the research presented in the paper ["Topological Tail Dependence: Evidence from Forecasting Realized Volatility"](https://doi.org/10.1016/j.jfds.2023.100107) and [repositoy](https://github.com/hugogobato/Topological-Tail-Dependence-Evidence-from-Forecasting-Realized-Volatility) by Hugo Gobato Souto. The package is designed to implement the methodologies and techniques described in the paper, focusing on the application of topological data analysis to understand tail dependence in financial markets.



The core of this package lies in its ability to model and forecast realized volatility in financial markets through the lens of topological data analysis. It presents a novel approach to understanding the complex relationships in financial data, especially during periods of high volatility or market stress.



# Installation



```cmd

> pip install fintda

```



You can also install the stable version with



```cmd



>>> pip install https://github.com/ibaris/finance-tda/archive/main.zip



```



To install the in-development version, change the branch name main to the other available branch names.



# Documentation



The documentation `code` documentation is in `build/docs`.



# Example



## Setup and Data Retrieval



Import Libraries: Import necessary libraries, including numpy, yfinance, and modules from the FinTDA package.



```python

import numpy as np

import yfinance as yf

from fintda import FinTDA

%matplotlib inline

```



Define Financial Indexes and Date Range: Select the financial indexes and the date range for analysis.



```python

index_names = ['^GSPC', '^DJI', '^RUT']  # S&P 500, Dow Jones, Russell 2000

start_date_string = "2000-01-01"

end_date_string = "2022-03-30"

```



Retrieve Data from Yahoo Finance: Use yfinance to download historical data for the specified indexes and date range.



```python

raw_data = yf.download(index_names, start=start_date_string, end=end_date_string)

```



```console

[*********************100%%**********************]  3 of 3 completed

```



Data Preprocessing: Focus on adjusted closing prices and compute logarithmic returns.



```python

df_close = raw_data['Adj Close'].dropna(axis='rows')

returns = np.log(df_close.pct_change() + 1)

returns.dropna(inplace=True)

```



## Financial Time Series Analysis with FinTDA



Initialize FinTDA: Create an instance of FinTDA with the processed returns and predefined weights. If the weights are None, then the weights will be equal to 1/n, where n is the number of assets in the portfolio. Moreover, if the sum of the weights is not equal to 1, then the weights will be normalized to sum to 1.



```python

weights = np.array([0.5, 0.3, 0.2])  # Define portfolio weights.

ftda = FinTDA(returns, weights)

```



```console

Rips(maxdim=2, thresh=inf, coeff=2, do_cocycles=False, n_perm = None, verbose=True)

```



Compute Moving Persistence Diagrams: Use the compute_moving_dgm method to calculate persistence diagrams. This method is essential for analyzing the topological features of the financial time series data.



```python

distance = ftda.compute_moving_dgm(plot=True)

```



```console

Computing Moving Diagrams: 100%|██████████| 5556/5556 [00:09<00:00, 580.01it/s]

```






# Reference



The development of this package is based on the research published in **\*the\*\*** following paper:



Souto, H.G. (2023). Topological Tail Dependence: Evidence from Forecasting Realized Volatility. The Journal of Finance and Data Science, 9. DOI: [10.1016/j.jfds.2023.100107](https://doi.org/10.1016/j.jfds.2023.10010)



The initial implementation from `hugogobato` can be found at:

[Topological Tail-Dependence Evidence](https://github.com/hugogobato/Topological-Tail-Dependence-Evidence-from-Forecasting-Realized-Volatility?tab=readme-ov-file)