# PyMC Help Needed - TVP-PVAR with Stochastic Volatility

**URL:** <https://discourse.pymc.io/t/pymc-help-needed-tvp-pvar-with-stochastic-volatility/14691>\
**Category:** v5\
**Tags:** development, gaussian\_process, modeling\
**Created:** [June 29, 2024, 1:51am UTC](https://discourse.pymc.io/t/pymc-help-needed-tvp-pvar-with-stochastic-volatility/14691 "2024-06-29T01:51:23Z")\
**Posts on this page:** 1\
**Page:** 1

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**Author:** ![D\_K](https://yyz2.discourse-cdn.com/flex036/user_avatar/discourse.pymc.io/d_k/32/8159_2.png) [@D\_K](https://discourse.pymc.io/u/D_K)\
**Post date:** [June 29, 2024, 1:51am UTC](https://discourse.pymc.io/t/pymc-help-needed-tvp-pvar-with-stochastic-volatility/14691/1 "2024-06-29T01:51:24Z")

</div>

Hi everyone,

I’m following up on a previous inquiry where @jessegrabowski (thanks again!) offered valuable help regarding a time-varying parameter panel vector autoregression _(TVP-PVAR)_ model with autoregressive order 1 _(AR(1))_ and stochastic volatility for my research (not yet published). I’m hoping to get some additional guidance from the community on the PyMC implementation aspects.

**Model Structure Description:**

My model leverages a state-space framework, a common approach for _TVP-PVAR_ models. This framework involves two key equations:

Observation Equation: This equation relates the observed data (denoted as _y\_t for time_ t) to a time-varying state vector (alpha\_t) and an error term _(varepsilon\_t)_. It captures how the observed data is generated by the underlying dynamics in the model.

State Evolution Equation: This equation describes how the state vector _(alpha\_t)_ evolves over time. It often involves the previous state vector _(alpha\_(t-1))_ and potentially a random component (eta\_t) to account for the time-varying nature of the parameters.

**Time-Varying Parameters and Stochastic Volatility:**

A key feature of my model is that some parameters within the state vector _(alpha\_t)_ can vary over time. This allows the model to capture the dynamic relationships between economic variables.

Additionally, the model incorporates stochastic volatility, meaning the variance of the error term _(varepsilon\_t)_ is not constant but can fluctuate over time.

**Specific Areas for Assistance (PyMC Implementation):**

I have tried as @jessegrabowski suggested [here](https://discourse.pymc.io/t/help-needed-kalman-filter-with-pymc-and-pytensor-tensor-kalmanfilter-error/14640/2), but I have not been successful  
I’m particularly interested in the following aspects of the PyMC implementation:

State-Space Model Setup: Recommendations for building the state-space model structure within PyMC, including defining placeholders for the state vector, observation equation, and state evolution equation.

Time-Varying Parameter Priors: Suggestions on appropriate prior distributions for these time-varying parameters within the state vector in a PyMC context (e.g., conjugate priors).

Stochastic Volatility Implementation: Insights on incorporating stochastic volatility into the model using PyMC, considering different approaches for modeling time-varying variances (e.g., concepts like random walk ).

**Additional Information :**

My model is related to Bayesian analysis, panel data, and time series econometrics.

I’m particularly interested in using PyMC for the implementation due to its capabilities in state-space modeling.

**Minimal Code Snippet (for Context):**

```python
import pymc as pm

class BayesianModel:

    def __init__ (self, data, vars):
        # data processing and initialization

    def process_country(self, country, filtered_data, vars):
        # Data filtering for a country

    with pm.Model() as model:
        # PyMC model building using state-space framework

    # Placeholder for state vector (alpha_t)

    # Placeholder for observation equation (relating y_t to alpha_t and error)

    # Placeholder for state evolution equation (how alpha_t evolves)

    # Sampling using MCMC methods (e.g., pm.sample)

    return country, trace

# Rest of the code for processing countries and analysis)

```

**Error Encountered (Context for process\_country function):**

Furthermore, I have tried some code ,but I’m encountering an error message within the process\_country function of my code. The error states: “_Error processing n must be an integer. It is a tensor_.” I’m using PyTensor throughout my code, and I suspect this error might be related to the usage of tensors where an integer value is expected.

I would greatly appreciate any guidance or suggestions you can offer to help me resolve these.

_Thank you in advance for your time and assistance!_

Sincerely,

Dimitri