GARCH models implementation in Pytorch

Implementing a GARCH model using PyTorch involves defining the architecture, loss function, and optimization steps. Here’s an example of how you can implement a GARCH(1, 1) model in PyTorch:

import torch
import torch.nn as nn
import torch.optim as optim
import numpy as np

# Define the GARCH(1, 1) model
class GARCH(nn.Module):
    def __init__(self):
        super(GARCH, self).__init__()
        self.alpha = nn.Parameter(torch.tensor(0.1))
        self.beta = nn.Parameter(torch.tensor(0.8))
        self.omega = nn.Parameter(torch.tensor(0.1))

    def forward(self, returns):
        conditional_variance = torch.var(returns)
        for i in range(1, len(returns)):
            error = returns[i-1] - torch.mean(returns)
            conditional_variance = self.omega + self.alpha * error**2 + self.beta * conditional_variance

        return conditional_variance

# Generate some random returns for demonstration
returns = np.random.normal(0, 1, size=100)

# Convert the returns to a PyTorch tensor
returns_torch = torch.tensor(returns, dtype=torch.float32)

# Create an instance of the GARCH model
model = GARCH()

# Define the loss function
criterion = nn.MSELoss()

# Define the optimizer
optimizer = optim.SGD(model.parameters(), lr=0.01)

# Training loop
for epoch in range(100):
    # Zero the gradients
    optimizer.zero_grad()

    # Forward pass
    conditional_variance = model(returns_torch)

    # Calculate the loss
    loss = criterion(conditional_variance, torch.zeros(1))

    # Backward pass
    loss.backward()

    # Update the weights
    optimizer.step()

# Get the final conditional variance
final_cv = model(returns_torch).item()

print("Final Conditional Variance:", final_cv)

In this example, we define a class GARCH that inherits from nn.Module, representing the GARCH(1, 1) model. Inside the class, we define the model parameters (alpha, beta, and omega) as nn.Parameter objects. The forward method performs the forward pass calculation, iterating through the returns and updating the conditional variance.

We generate some random returns for demonstration purposes and convert them to a PyTorch tensor. We then create an instance of the GARCH model, define the loss function (MSE), and the optimizer (SGD).

In the training loop, we iterate for a specified number of epochs. In each epoch, we perform a forward pass, calculate the loss, perform a backward pass, and update the weights using the optimizer.

Finally, we get the final conditional variance by passing the returns tensor through the model and extract the value using the item() method.

Please note that this implementation is a simplified example, and real-world GARCH models may involve additional complexity, such as additional layers, time-varying parameters, or more sophisticated optimization algorithms. You can customize and enhance this implementation based on your specific requirements.