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aibit0111 committed Dec 4, 2024
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Example: VAR(2) process
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In this example, we demonstrate how to implement and perform Bayesian inference for a
Vector Autoregressive process of order 2 (VAR(2)). VAR models are widely used in
In this example, we demonstrate how to implement and perform Bayesian inference for a
Vector Autoregressive process of order 2 (VAR(2)). VAR models are widely used in
time series analysis, especially for capturing the dynamics between multiple variables.
A VAR(2) process for a multivariate time series :math:`y_t` with :math:`K` variables is defined as:
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y_t = c + \Phi_1 y_{t-1} + \Phi_2 y_{t-2} + \epsilon_t
Here, :math:`c` is a constant vector, :math:`\Phi_1` and :math:`\Phi_2` are coefficient matrices for lag 1
and lag 2, respectively, and :math:`\epsilon_t` is a Gaussian noise term with zero mean and a
Here, :math:`c` is a constant vector, :math:`\Phi_1` and :math:`\Phi_2` are coefficient matrices for lag 1
and lag 2, respectively, and :math:`\epsilon_t` is a Gaussian noise term with zero mean and a
covariance matrix :math:`\Sigma`.
This example uses NumPyro's `scan` utility to efficiently model the temporal dependencies without
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