Inference theory for volatility functional dependencies

Jia Li, Viktor Todorov, George Tauchen*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


We develop inference theory for models involving possibly nonlinear transforms of the elements of the spot covariance matrix of a multivariate continuous-time process observed at high frequency. The framework can be used to study the relationship among the elements of the latent spot covariance matrix and processes defined on the basis of it such as systematic and idiosyncratic variances, factor betas and correlations on a fixed interval of time. The estimation is based on matching model-implied moment conditions under the occupation measure induced by the spot covariance process. We prove consistency and asymptotic mixed normality of our estimator of the (random) coefficients in the volatility model and further develop model specification tests. We apply our inference methods to study variance and correlation risks in nine sector portfolios comprising the S&P 500 index. We document sector-specific variance risks in addition to that of the market and time-varying heterogeneous correlation risk among the market-neutral components of the sector portfolio returns.

Original languageEnglish (US)
Pages (from-to)17-34
Number of pages18
JournalJournal of Econometrics
Issue number1
StatePublished - Jul 1 2016


  • High-frequency data
  • Occupation measure
  • Semimartingale
  • Specification test
  • Stochastic volatility

ASJC Scopus subject areas

  • Economics and Econometrics


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