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Factor multivariate stochastic volatility models of high dimension

Benjamin Poignard, Manabu Asai

Abstract

Building upon factor decomposition to overcome the curse of dimensionality inherent in multivariate volatility processes, we develop a factor model-based multivariate stochastic volatility (fMSV) framework. We propose a two-stage estimation procedure for the fMSV model: in the first stage, estimators of the factor model are obtained, and in the second stage, the MSV component is estimated using the estimated common factor variables. We derive the asymptotic properties of the estimators, taking into account the estimation of the factor variables. The prediction performances are illustrated by finite-sample simulation experiments and applications to portfolio allocation.

Factor multivariate stochastic volatility models of high dimension

Abstract

Building upon factor decomposition to overcome the curse of dimensionality inherent in multivariate volatility processes, we develop a factor model-based multivariate stochastic volatility (fMSV) framework. We propose a two-stage estimation procedure for the fMSV model: in the first stage, estimators of the factor model are obtained, and in the second stage, the MSV component is estimated using the estimated common factor variables. We derive the asymptotic properties of the estimators, taking into account the estimation of the factor variables. The prediction performances are illustrated by finite-sample simulation experiments and applications to portfolio allocation.

Paper Structure

This paper contains 25 sections, 4 theorems, 90 equations, 1 figure, 5 tables.

Table of Contents

  1. Introduction
  2. fMSV Model
  3. Estimation
  4. Estimation of the factor model
  5. Estimation of the MSV parameters
  6. Simulations
  7. Data generating processes
  8. Measures for statistical accuracy
  9. Competing models
  10. Results
  11. Out-of-sample analysis with real data
  12. Data
  13. Statistical accuracy and portfolio allocation
  14. Conclusion
  15. Asymptotic properties
  16. ...and 10 more sections

Key Result

Theorem A.1

Under Assumptions assumption_unif_consistency_factors-assumption_ell_F_control_gradient_hessian, $\sqrt{q}b_{T,p} \rightarrow 0$, $q^4b^2_{T,p}=o(T)$, there exists a sequence $(\widetilde{\theta}_1)$ of solutions of (obj_crit_first_estimator) that satisfies $\|\widetilde{\theta}_1-\theta_{01}\|_2 =

Figures (1)

  • Figure 1: Computation time

Theorems & Definitions (9)

  • Theorem A.1
  • Remark A.1
  • proof : Proof of Theorem \ref{['bound_proba_first_step_estimator']}
  • Theorem A.2
  • proof : Proof of Theorem \ref{['bound_prob_asym']}.
  • Theorem A.3
  • proof : Proof of Theorem \ref{['sparsistency']}.
  • Theorem A.4
  • proof : Proof of Theorem \ref{['bound_proba_second_step_estimator']}.