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Multiple Univariate ARCH modeling toolbox built on top of the ARCH package

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Install and update using pip and on conda.

This is a wrapper on top of Kevin Sheppard's ARCH package. The purpose of which are to:

  1. Enable faster Monte Carlo simulation
  2. Simulate innovations through copula marginals

In the package, there are 2 classes to aid you - UArch and MUArch. The UArch class can be defined using a similar API to arch_model in the original arch package. The MUArch is a collection of these UArch models.

Thus, if you have a function that generates uniform marginals, like a copula, you can create a dependence structure among the different marginals when simulating the GARCH processes.

If you need a copula package, I have one here. :)


I'll list out a simple procedure to do AR-GARCH-Copula simulations.

from muarch import MUArch, UArch
from muarch.datasets import load_etf
from copulae import NormalCopula

returns = load_etf()  # load returns data
num_assets = returns.shape[1]

# sets up a MUArch model collection where each model defaults to 
# mean: AR(1)
# vol: GARCH(1, 1)
# dist: normal 
models = MUArch(num_assets, mean='AR', lags=1) 

# set first model to AR(1)-GARCH(1, 1) with skewt innovations  
models[0] = UArch('AR', lags=1, dist='skewt')  

# fit model, if you get complaints regarding non-convergence, you can scale the data up 
# using the scale parameter in the UArch or MUArch. i.e. UArch(..., scale=100). This will
# reduce numerical errors. Don't worry, I'll rescale the simulation values subsequently

# Usually you'll want to fit the residuals to the copula, use the copula to generate the
# residuals and subsequently transform it back to returns 

residuals = models.residuals() # defaults to return the standardized residuals

cop = NormalCopula(dim=num_assets) # use a normal copula, you could of course use a TCopula

# simulate 10 steps into the future, over 4 repetitions. This will return a (10 x 4 x 3) array
models.simulate_mc(10, 4, custom_dist=cop.random)

Future Works

This is actually a temporary hack so that others can do GARCH copula simulation. Another issue is that an ARFIMA mean model is not so easily specified (and simulated from) with the original arch package. You could specify an ARFIMA (or even just an ARMA model for the matter), fit it separately then use the residuals to fit a zero-mean model (pure GARCH). However, in such a way, the simulation is not so straightforward as you'll have to stitch the simulations from GARCH process and the mean model process back.

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