TVPVARConnectedness

A lightweight Python implementation of time varying parameter VAR (TVP-VAR) with discount factors and Diebold–Yilmaz style connectedness measures, following Antonakakis et al. (2020).

The core class TVPVARConnectedness estimates a TVP-VAR with forgetting factors, computes generalized forecast error variance decompositions (GFEVDs), and provides a rich set of tools to study time varying connectedness:

• Total Connectedness Index (TCI)
• Directional connectedness TO and FROM others and net directional connectedness
• Net pairwise directional connectedness
• Static Diebold–Yilmaz table averaged over time
• Time series plots, pairwise plots, and network graphs (gross and net) of the connectedness measures

All of this lives in a single file, TVPVARConnectedness.py, with no heavy dependencies beyond NumPy, pandas and matplotlib. Network graphs are optional and only require networkx.

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Features

• TVP-VAR(p) estimated via discounted Kalman filter with:
  • Discount factor kappa1 for state covariance
  • Discount factor kappa2 for innovation covariance
• OLS VAR prior estimated on an initial window (prior_length)
• Time varying GFEVDs at a user set forecast horizon H
• Standard Diebold–Yilmaz connectedness measures:
  • Total Connectedness Index (TCI)
  • Directional TO, FROM and NET connectedness
  • Net pairwise directional connectedness
• Convenience methods that return pandas objects:
  • get_tci()
  • get_directional()
  • get_static_table() and get_static_table_df()
  • get_pairwise_directional()
  • get_net_pairwise()
• Plotting helpers:
  • plot_tci()
  • plot_directional_subplots() for TO, FROM, or net FROM others
  • plot_pairwise_directional_subplots() for pairwise directional connectedness
  • plot_net_pairwise_subplots() for net pairwise connectedness
  • plot_network() and plot_network_panel() for gross and net network graphs at selected dates

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Installation

For now this is a single-file module. You can use it in two simple ways.

Option 1: Drop-in file

1. Download TVPVARConnectedness.py into your project.
2. Import the class:

from TVPVARConnectedness import TVPVARConnectedness

Make sure the file is on your Python path (for example in the same folder as your script or added to PYTHONPATH).

Option 2: Install from GitHub

Once the repository is public you can install directly via pip:

pip install git+https://github.com/Lewispy/TVPVARConnectedness.git

Then import as usual:

from TVPVARConnectedness import TVPVARConnectedness

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Requirements

• Python 3.8 or later
• NumPy
• pandas
• matplotlib

For network graphs:

• networkx (optional but recommended)

If networkx is not installed, calling plot_network or plot_network_panel will raise a clear error message asking you to install it.

Install the core dependencies with:

pip install numpy pandas matplotlib

and optionally:

pip install networkx

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Quick start

Here is a minimal example using a pandas DataFrame of excess returns.

import numpy as np
import pandas as pd
from TVPVARConnectedness import TVPVARConnectedness

# Suppose df is a DataFrame of T daily observations with columns:
# ["Y1", "Y2", "Y3", "Y4", "Y5", "Y6"]
# and a DateTimeIndex.
y = df[["Y1", "Y2", "Y3", "Y4", "Y5", "Y6"]].values
dates = df.index.to_numpy()

# 1. Estimate TVP-VAR(1) with 10-step horizon and 1-year prior window
model = TVPVARConnectedness(
    y=y,
    lags=1,
    horizon=10,
    kappa1=0.99,
    kappa2=0.96,
    prior_length=252,
    dates=dates,
).fit()

# 2. Total Connectedness Index
tci = model.get_tci()              # pandas Series
fig, ax = model.plot_tci()

# 3. Directional connectedness
to_df, from_df, net_df = model.get_directional()
fig, axes = model.plot_directional_subplots(
    which="to",
    labels=["Y1", "Y2", "Y3", "Y4", "Y5", "Y6"],
)

# 4. Static Diebold–Yilmaz table
static_table = model.get_static_table_df(
    labels=["Y1", "Y2", "Y3", "Y4", "Y5", "Y6"]
)
print(static_table.round(2))

# 5. Network graphs at selected dates (requires networkx)
#    Example: last date, and two dates around interesting events
fig, axes = model.plot_network_panel(
    times=["2021-03-01", "2022-03-01", "2023-03-01", -1],
    labels=[""Y1", "Y2", "Y3", "Y4", "Y5", "Y6"],
    use_net=False,           # gross network; set True for net pairwise
    threshold=1.0,
)

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API overview

Only the main methods are listed here. See the docstrings in TVPVARConnectedness.py for full details.

Estimation

TVPVARConnectedness(y, lags=1, horizon=10,
                    kappa1=0.99, kappa2=0.96,
                    prior_length=None, dates=None)

model.fit()

• y – array of shape (T, m) with T observations of m variables.
• lags – VAR order p.
• horizon – forecast horizon H for GFEVD.
• kappa1 – discount factor for the state covariance (0 < kappa1 ≤ 1).
• kappa2 – discount factor for the innovation covariance (0 < kappa2 ≤ 1).
• prior_length – length of initial sample used for OLS VAR prior. If None, a reasonable default is chosen.
• dates – optional time index of length T (for pandas outputs and axis labels).

Connectedness measures

• get_tci()
  Returns a pandas Series with the Total Connectedness Index over time.

• get_directional()
  Returns three DataFrames (to_df, from_df, net_df) with directional TO, FROM, and NET connectedness for each variable.

• get_static_table()
  Returns a dictionary with average GFEVD and connectedness statistics.

• get_static_table_df(labels=None)
  Returns a Diebold–Yilmaz style static table as a pandas DataFrame with rows and columns corresponding to variables plus TO/FROM/NET and the average TCI.

• get_pairwise_directional(from_idx, to_idx, labels=None)
  Time series of directional connectedness FROM variable from_idx TO variable to_idx.

• get_net_pairwise(i, j, labels=None)
  Time series of net pairwise directional connectedness between variables i and j (> 0 means j is net transmitter to i).

Plotting helpers

• plot_tci(ax=None)
• plot_directional_subplots(which="to", labels=None, figsize=(14, 8))
• plot_pairwise_directional_subplots(which="both", labels=None, figsize=(16, 10))
• plot_net_pairwise_subplots(labels=None, figsize=(16, 10))
• plot_network(t_idx=-1, labels=None, threshold=1.0, use_net=False, figsize=(8, 8), ax=None)
• plot_network_panel(times, labels=None, threshold=1.0, use_net=False, figsize_per_plot=(5.0, 5.0))

These functions all return the figure and axes, so you can further customise or save them.

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References

If you use this code in academic work, please consider citing the underlying connectedness literature, for example:

• Diebold, F. X., & Yilmaz, K. (2014). On the network topology of variance decompositions: Measuring the connectedness of financial firms. Journal of Econometrics, 182(1), 119–134.
• Antonakakis, N., Chatziantoniou, I., & Gabauer, D. (2020). Refined measures of dynamic connectedness based on TVP-VAR. Journal of Risk and Financial Management, 18(34).

You may also acknowledge the GitHub repository implementing this TVP-VAR connectedness class.

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License

This project is licensed under the MIT License. See the LICENSE file for details.