ccmm_sv

CCMM Stochastic Volatility VAR with Random Walk Heteroscedasticity (CCMMSV)

Overview

The CCMM Stochastic Volatility VAR implements the framework developed by Chan, Koop, Poirier, and Tobias. This estimator features constant VAR coefficients with stochastic volatility that follows random walk processes, providing a robust approach to modeling time-varying uncertainty with smooth, persistent volatility changes.

Methodology

The CCMMSV specification features:

• Constant VAR coefficients with Minnesota-type priors
• Stochastic volatility following random walk processes
• Smooth volatility evolution without jumps or outliers
• Efficient MCMC algorithms tailored for the CCMM framework
• Focus on persistent, gradual volatility changes

This approach is particularly suitable when volatility changes are expected to be smooth and persistent rather than abrupt.

Parameters

Minnesota-Style Prior Parameters

• Autoregression: Prior on first-order autoregression

  • Range: [0, 1]
  • Default: 0.8
  • Controls the belief in random walk behavior for own lags

• Lambda1: Overall tightness of priors

  • Range: (0, ∞)
  • Default: 0.1
  • Smaller values impose tighter priors (more shrinkage)

• Lambda2: Variable weighting

  • Range: (0, ∞)
  • Default: 0.5
  • Controls relative weights between own-variable and cross-variable lags

• Lambda3: Lag decay

  • Range: (0, ∞)
  • Default: 1
  • Controls how quickly prior importance decays with lag length

• Lambda4: Exogenous variable tightness

  • Range: (0, ∞)
  • Default: 100
  • Controls prior tightness on exogenous variable coefficients

• Lambda5: Block exogeneity shrinkage

  • Range: (0, ∞)
  • Default: 0.001
  • Controls shrinkage when block exogeneity is imposed

CCMM-Specific Parameters

• HeteroskedasticityScale: Scaling factor for IW distribution of heteroscedasticity parameter

  • Range: (0, ∞)
  • Default: 0.15
  • Controls the prior scaling of the volatility process

• Turningpoint: Latest point of range for getting mean prior for B matrix

  • Type: Date
  • Default: "" (empty)
  • Controls the training sample end point for prior construction

Advanced Options

• Exogenous: Priors on exogenous variables flag

  • Default: false
  • Enables specialized priors for exogenous variables

• BlockExogenous: Block exogeneity flag

  • Default: false
  • Imposes block exogeneity restrictions

MCMC Settings

• Burnin: Number of burn-in draws

  • Range: [0, ∞)
  • Default: 0
  • Recommended: Several thousand for proper convergence

• StabilityThreshold: Threshold for maximum eigenvalue magnitude

  • Range: (0, ∞)
  • Default: null (no stability check)
  • Ensures VAR stability by rejecting draws with eigenvalues above threshold

• MaxNumUnstableAttempts: Maximum number of unstable sampling attempts

  • Range: [1, ∞)
  • Default: 1000
  • Maximum attempts to find stable draw before stopping

Usage Guidelines

When to Use

• Smooth volatility evolution: When volatility changes are persistent and gradual
• Financial time series: Modeling asset returns with time-varying volatility
• Moderate volatility changes: When extreme volatility spikes are not the primary concern
• Robust volatility modeling: When seeking a well-established stochastic volatility approach

When Not to Use

• Volatility jumps: When sudden volatility changes are important (use CCMMSVOT)
• Outlier periods: When occasional extreme observations need special treatment (use CCMMSVO)
• Constant volatility: When volatility is stable over time
• Parameter instability: When coefficient changes are the primary concern

Practical Considerations

• Consider the heteroscedasticity scale parameter carefully - it affects volatility smoothness
• The turning point parameter can be useful for out-of-sample applications
• Monitor volatility evolution for economic interpretability
• Compare with simpler constant volatility models for model selection

Model Specification

Observation Equation

y_t = X_t β + A^{-1} Σ_t^{1/2} ε_t

where β are constant and Σ_t follows stochastic volatility.

Volatility Process

Log volatilities follow random walks:

log(σ²_{i,t}) = log(σ²_{i,t-1}) + η_{i,t}

where η_{i,t} ~ N(0, γᵢ) with careful prior specification.

Computational Characteristics

Performance

• Speed: Moderate computational requirements
• Memory: Standard memory usage for stochastic volatility models
• Convergence: Generally good convergence with proper tuning
• Stability: Numerically stable with appropriate prior settings

CCMM Framework Benefits

• Efficient posterior simulation algorithms
• Well-tested implementation
• Good handling of volatility identification
• Robust to various data characteristics

Comparison with Related Models

vs. Cogley-Sargent SV

• Framework: CCMM vs. Cogley-Sargent methodology
• Implementation: Different posterior simulation approaches
• Performance: Comparable performance with different computational characteristics
• Usage: Alternative robust stochastic volatility specification

vs. CCMM with Outliers/Jumps

• Scope: Smooth volatility vs. accommodating extreme events
• Complexity: Simpler than outlier-robust variants
• Robustness: Less robust to extreme observations
• Speed: Faster than more complex CCMM variants

Implementation Notes

Prior Considerations

• The heteroscedasticity scale parameter significantly affects results
• Turning point selection impacts prior construction when specified
• Minnesota parameters control coefficient shrinkage as in standard VARs
• Consider data characteristics when setting volatility priors

Convergence Assessment

• Monitor volatility parameter convergence carefully
• Check for proper mixing in MCMC chains
• Assess autocorrelation in posterior draws
• Validate volatility estimates against data features

References

• Chan, J.C.C., G. Koop, R.W. Poirier, and J.L. Tobias (2019). "A New Model of Trend Inflation"
• Koop, G. and D. Korobilis (2013). "Large Time-Varying Parameter VARs"
• Primiceri, G.E. (2005). "Time Varying Structural Vector Autoregressions and Monetary Policy"