# Ordinary Least Squares (`Ordinary`)

## Description
Classical ordinary least squares (OLS) estimation without priors. This is the baseline VAR estimator that provides maximum likelihood estimates through equation-by-equation OLS regression.

## Technical Details
- Uses equation-by-equation OLS estimation
- No prior information incorporated
- Posterior sampling available for uncertainty quantification
- Can be used as benchmark for comparison with Bayesian estimators

## User Settings (Hyperparameters)

### Core Settings

#### `FixedBeta` (logical)
- **Description**: Keep VAR coefficients fixed when sampling from posterior distribution
- **Default**: `false`
- **Details**: When set to `true`, the coefficient matrix β is held constant at its OLS estimate during posterior sampling, eliminating parameter uncertainty for coefficients

#### `FixedSigma` (logical)  
- **Description**: Keep error covariance matrix fixed when sampling from posterior distribution
- **Default**: `false`
- **Details**: When set to `true`, the error covariance matrix Σ is held constant at its OLS estimate during posterior sampling, eliminating parameter uncertainty for error variances

### Inherited Base Settings

#### `Burnin` (double)
- **Description**: Number of burn-in draws for posterior sampling
- **Default**: `0`
- **Details**: Number of initial MCMC draws to discard before collecting posterior samples

#### `StabilityThreshold` (double)
- **Description**: Threshold for maximum eigenvalue magnitude to ensure VAR stability
- **Default**: `Inf` (no stability check)
- **Details**: Maximum allowed eigenvalue magnitude; draws with eigenvalues exceeding this are rejected

#### `MaxNumUnstableAttempts` (double)
- **Description**: Maximum number of unstable sampling attempts before giving up
- **Default**: `1000`
- **Details**: If stability checking is enabled, this limits the number of consecutive unstable draws before termination


## Usage Notes
- Primary use case is as a benchmark for comparison with Bayesian estimators
- Provides classical statistical inference through asymptotic theory
- No prior information incorporated, so results depend entirely on sample data
- Only has two specific settings (`FixedBeta` and `FixedSigma`) plus standard sampling control parameters
- When both `FixedBeta` and `FixedSigma` are `true`, posterior sampling reduces to point estimates