Practical Options for Fitting Multivariate GARCH Models
Summary
The document surveys ways to estimate multivariate conditional volatility when a Python workflow is desired. It notes that common Python GARCH support may focus on univariate models, and suggests that a basic multivariate model could require custom implementation, using existing univariate routines as a starting point. It also identifies R packages for multivariate GARCH, including tools for DCC models and related univariate specifications.
One example connects Python return data to R, fits a DCC-GARCH model, forecasts covariance matrices, and aggregates those forecasts across the forecast horizon. Another answer mentions a Python package supporting DCC-GARCH(1,1) under multivariate normal and Student distributions. These are pointers and an illustrative workflow, not a benchmark or a guarantee of current package support. Users should check package maintenance, model assumptions, data conversion behavior, and whether summing covariance forecasts suits the portfolio horizon they need.
Key ideas
- Multivariate GARCH models estimate time-varying volatility and covariance across return series.
- The document describes Python and R as possible parts of an estimation workflow.
- A DCC-GARCH approach combines individual volatility models with dynamic correlation estimates.
- Forecast covariance matrices can be aggregated across days for a multi-day covariance estimate.
- Package availability and model capabilities should be checked before relying on the suggested tools.
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Full text
# Multivariate GARCH in Python
# Multivariate GARCH in Python
Is there a package to run simplified multivariate GARCH models in Python? I found the Arch package but that seems to work on only univariate models. I'd like to test out some of the more simple methods described in Bauwens et. al. (2006) like constant conditional correlation.
Python libraries are preferred though I'll play with R as well.
## Answer by Robert Szóstakowski (score 4, accepted)
https://quant.stackexchange.com/a/20688
PYTHON I have found this class from the statsmodels library for calculating Garch models. Unfortunately, I have not seen MGARCH class/library. Below you can see the basic information about the garch models in mentioned class from the statsmodels. Probably you have to implement it by your own in python, so this class might be used as a starting point.
> roadmap for garch: * simple case * starting values: garch11 explicit formulas * arma-garch, assumed separable, blockdiagonal Hessian * other standard garch: egarch, pgarch, * non-normal distributions * other methods: forecast, news impact curves (impulse response)
R In R there is a package called mgarch which is available in this github repository and here you can find some examples.
## Answer by Bowen Cao (score 3)
https://quant.stackexchange.com/a/53203
I recently met the same problem and found a way to achieve it using R in Python.
```
from rpy2.robjects import pandas2ri
import rpy2.robjects as objects
import numpy as np
# pd_rets - a pandas dataframe of daily returns, where the column names are the tickers of stocks and index is the trading days.
# compute DCC-Garch in R using rmgarch package
pandas2ri.activate()
r_rets = pandas2ri.py2ri(pd_rets) # convert the daily returns from pandas dataframe in Python to dataframe in R
r_dccgarch_code = """
library('rmgarch')
function(r_rets, n_days){
univariate_spec <- ugarchspec(mean.model = list(armaOrder = c(0,0)),
variance.model = list(garchOrder = c(1,1),
variance.targeting = FALSE,
model = "sGARCH"),
distribution.model = "norm")
n <- dim(r_rets)[2]
dcc_spec <- dccspec(uspec = multispec(replicate(n, univariate_spec)),
dccOrder = c(1,1),
distribution = "mvnorm")
dcc_fit <- dccfit(dcc_spec, data=r_rets)
forecasts <- dccforecast(dcc_fit, n.ahead = n_days)
list(dcc_fit, forecasts@mforecast$H)
}
"""
r_dccgarch = robjects.r(r_dccgarch_code)
r_res = r_dccgarch(r_rets,n_days)
pandas2ri.deactivate()
# end of R
r_dccgarch_model = r_res[0] # model parameters
r_forecast_cov = r_res[1] # forecasted covariance matrices for n_days
# access and transform the covariance matrices in R format
n_cols = pd_rets.shape[1] # get the number of stocks in pd_rets
n_elements = n_cols*n_cols # the number of elements in each covariance matrix
n_matrix = int(len(r_forecast_cov[0])/(n_elements))
print(n_matrix) # this should be equal to n_days
# sum the daily forecasted covariance matrices
cov_matrix = 0
for i in range(n_matrix):
i_matrix = np.array([v for v in r_forecast_cov[0][i*n_elements:(i+1)*n_elements]])
i_matrix = i_matrix.reshape(n_cols,n_cols)
cov_matrix += i_matrix
```
## Answer by Oleg Melnikov (score 2)
https://quant.stackexchange.com/a/21704
Slight correction: the package in R is called `rmgarch`, not `mgarch`. It works well with `rugarch`, which provides a variety of univariate GARCH models. Both packages allow for parallelized computation on local cluster and return a nice and full set of fitted parameters, model specs, etc. I provided some additional links in this post.
## Answer by Faisal Nawaz (score 1)
https://quant.stackexchange.com/a/58611
mgarch is a python package for predicting volatility of daily returns in financial markets.
DCC-GARCH(1,1) for multivariate normal and student t. distribution.Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.