Equation-by-Equation Estimation of a Multivariate Log-GARCH-X Model of Financial Returns

Francq, Christian and Sucarrat, Genaro (2015): Equation-by-Equation Estimation of a Multivariate Log-GARCH-X Model of Financial Returns.

Abstract

Estimation of large financial volatility models is plagued by the curse of dimensionality: As the dimension grows, joint estimation of the parameters becomes infeasible in practice. This problem is compounded if covariates or conditioning variables (``X") are added to each volatility equation. In particular, the problem is especially acute for non-exponential volatility models (e.g. GARCH models), since there the variables and parameters are restricted to be positive. Here, we propose an estimator for a multivariate log-GARCH-X model that avoids these problems. The model allows for feedback among the equations, admits several stationary regressors as conditioning variables in the X-part (including leverage terms), and allows for time-varying covariances of unknown form. Strong consistency and asymptotic normality of an equation-by-equation least squares estimator is proved, and the results can be used to undertake inference both within and across equations. The flexibility and usefulness of the estimator is illustrated in two empirical applications.

• Item Type: MPRA Paper
• Language: English
• Keywords: Exponential GARCH, multivariate log-GARCH-X, VARMA-X, Equation-by-Equation Estimation (EBEE), Least Squares
• Subjects: C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C13 - Estimation: General; C - Mathematical and Quantitative Methods > C2 - Single Equation Models ; Single Variables > C22 - Time-Series Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes; C - Mathematical and Quantitative Methods > C3 - Multiple or Simultaneous Equation Models ; Multiple Variables > C32 - Time-Series Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes ; State Space Models; C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C51 - Model Construction and Estimation; C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C58 - Financial Econometrics

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