Shape Mismatch Issue in TVP-PVAR Model Implementation

[D. K]

 

Hello,

 I am reaching out to seek your expertise regarding a persistent issue I have encountered while implementing a Time-Varying Parameter Panel Vector Autoregression (TVP-PVAR) model. I have managed to write a such code and model. Despite several attempts to resolve the problem, I continue to face a shape mismatch error.

**Problem Description:**

The error message I receive is as follows:
```
Error at country 0, time 1: Dimension mismatch: array 'cov' is of shape (4, 4), but 'mean' is a vector of length 304.
Likelihood could not be calculated due to an error.
```
This occurs when using the `multivariate_normal.pdf` function from the `scipy.stats` module. The function expects the `mean` parameter to be a vector with a length equal to the number of rows (or columns) of the covariance matrix `R`.

**Relevant Code Section:**

Here is the part of the code where the issue arises:

```python
def likelihood(data, alphas, Phi, Q, R):
    n_countries, n_periods, n_vars = data.shape
    p = Phi.shape[2]
    total_obs = n_countries * n_periods * n_vars

    likelihood = 1
    for i in range(n_countries):
        for t in range(p, n_periods):
            y_it = data[i, t].ravel()
            y_hat = alphas[i] + np.sum([np.dot(data[i, t-j], Phi[i, j-1]) for j in range(1, p+1)], axis=0)
            y_hat_flat = y_hat.ravel()  # Flatten y_hat for compatibility

            try:
                likelihood *= multivariate_normal.pdf(y_it, mean=y_hat_flat, cov=R)
            except ValueError as e:
                print(f"Error at country {i}, time {t}: {e}")
                return None

    return likelihood
```

Despite ensuring that `y_it` and `y_hat` are flattened to 1D vectors, the mismatch persists. The current definition of `R` is as follows:
```python
R = np.eye(n_vars)  # Observation equation covariance matrix
```
Here, `R` is defined as the covariance matrix for the observation equation. Given that `n_vars` is 4, `R` is a 4x4 identity matrix.

**Steps Taken to Resolve the Issue:**

1. **Flattened `y_it` and `y_hat`:** Reshaped both `y_it` and `y_hat` to 1D vectors using `.ravel()`.
2. **Defined Compatible Shape for `R`:** Attempted to ensure `R` had a compatible shape with the length of `y_hat.ravel()`. Originally set `R` to `np.eye(n_vars)`, but considering the length of `y_hat.ravel()` is 304, a larger identity matrix was also tested.
3. **Print Statements for Debugging:** Added print statements to verify shapes of `y_it`, `y_hat`, and `R`.

Despite these efforts, the shape mismatch error persists. I suspect there might be a fundamental issue with the way `R` is being defined or used in the context of the likelihood calculation. I need to have the likelihood calculation explicitly calculated in the code.

**Request for Assistance:**

I have several blocks of variables for the model. For this example, I use 4 variables, reaching at a model of 28 variables. All variables are endogenous.

Could you please provide guidance on how to correctly define and use the covariance matrix `R` in this context? Any insights or suggestions on resolving the shape mismatch would be greatly appreciated.

Thank you for your time and assistance.

Best regards,

David K.