Francq, Christian and Sucarrat, Genaro (2015): EquationbyEquation Estimation of a Multivariate LogGARCHX Model of Financial Returns.

PDF
MPRA_paper_67140.pdf Download (673kB)  Preview 
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 nonexponential 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 logGARCHX model that avoids these problems. The model allows for feedback among the equations, admits several stationary regressors as conditioning variables in the Xpart (including leverage terms), and allows for timevarying covariances of unknown form. Strong consistency and asymptotic normality of an equationbyequation 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 

Original Title:  EquationbyEquation Estimation of a Multivariate LogGARCHX Model of Financial Returns 
English Title:  EquationbyEquation Estimation of a Multivariate LogGARCHX Model of Financial Returns 
Language:  English 
Keywords:  Exponential GARCH, multivariate logGARCHX, VARMAX, EquationbyEquation 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  TimeSeries Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes C  Mathematical and Quantitative Methods > C3  Multiple or Simultaneous Equation Models ; Multiple Variables > C32  TimeSeries 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 
Item ID:  67140 
Depositing User:  Dr. Genaro Sucarrat 
Date Deposited:  09. Oct 2015 18:12 
Last Modified:  09. Oct 2015 18:37 
References:  Aielli, G. P. (2013). Dynamic Conditional Correlations: On Properties and Estimation. Journal of Business and Economic Statistics 31, 282–299. http://dx.doi.org/10. 1080/07350015.2013.771027. Apergis, N. and A. Rezitis (2011). Food Price Volatility and Macroeconomic Factors: Evidence from GARCH and GARCHX Estimates. Journal of Agricultural and Applied Economics 43, 95–110. Bauwens, L., D. Rime, and G. Sucarrat (2006). Exchange Rate Volatility and the Mixture of Distribution Hypothesis. Empirical Economics 30, 889–911. Billingsley, P. (1961). Statistical methods in Markov chains. The Annals of Mathematical Statistics 32, 12–40. Bollerslev, T. and M. Melvin (1994). BidAsk spreads and the volatility in the foreign exchange market: An empirical analysis. Journal of International Economics 36, 355– 372. Boussama, F., F. Fuchs, and R. Stelzer (2011). Stationarity and Geometric Ergodicity of BEKK Multivariate GARCH Models. Stochastic Processes and Their Applications 121, 2331–2360. Brenner, R., R. Harjes, and K. Kroner (1996). Another look at models of the shortterm interest rate. Journal of Financial and Quantitative Analysis 31, 85–107. Chen, M. and Q. Song (2015). Semiparametric estimation and forecasting for exogenous logGARCH models. TEST. DOI: http://dx.doi.org/10.1007/s1174901504426. Clark, P. (1973). A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices. Econometrica 41, 135–155. Conrad, C. and E. Weber (2013). Measuring persistence in volatility spillovers. Discussion Paper 543, Department of Economics, University of Heidelberg. http://archiv.ub. uniheidelberg.de/volltextserver/14865/. Dominguez, K. M. (1998). Central bank interventions and exchange rate volatility. Journal of International Money and Finance 17, 161–190. Engle, R. (2002). Dynamic Conditional Correlation: A Simple Class of Multivariate Generalized Autoregressive Conditional Heteroskedasticity Models. Journal of Business and Economic Statistics 20, 339–350. Engle, R. and G. Gallo (2006). A multiple indicators model for volatility using intradaily data. Journal of Econometrics 131, 3–27. Francq, C. and G. Sucarrat (2013). An Exponential ChiSquared QMLE for LogGARCH Models Via the ARMA Representation. http://mpra.ub.unimuenchen.de/51783/. Francq, C. and L. Q. Thieu (2015). Qml inference for volatility models with covariates. http://mpra.ub.unimuenchen.de/63198/. Francq, C. and J.M. Zakoïan (2010). GARCH Models. New York: Marcel Dekker. Francq, C. and J.M. Zakoïan (2015). Estimating multivariate GARCH and stochastic correlation models equation by equation. Forthcoming in The Journal of the Royal Statistical Society. Series B. Working paper version: MPRA Paper No. 54250. Online at http://mpra.ub.unimuenchen.de/54250/. Garman, M. B. and M. J. Klass (1980). On the Estimation of Securities Price Volatilities from Historical Data. Journal of Business 53, 67–78. Hagiwara, M. and M. Herce (1999). Endogenous exchange rate volatility, trading volume and interest rate differentials in a model of portfolio selection. Review of International Economics 7, 202–218. Han, H. and D. Kristensen (2014). Asymptotic theory for the QMLE in GARCHX models with stationary and nonstationary covariates. Journal of Business and Economic Statistics, ??–?? Hansen, P. R., Z. Huan, and H. H. Shek (2012). Realized GARCH: A Joint Model for Returns and Realized Measures of Volatility. Journal of Applied Econometrics 27, 877–906. Hwang, S. and S. Satchell (2005). GARCH model with crosssectional volatility: GARCHX models. Applied Financial Economics 15, 203–216. Lamoureux, C. G. and W. D. Lastrapes (1990). Heteroscedasticity in Stock Return Data: Volume versus GARCH Effects. The Journal of Finance, 221–229. Nelson, D. B. (1991). Conditional Heteroskedasticity in Asset Returns: A New Approach. Econometrica 59, 347–370. Parkinson, M. (1980). The Extreme Value Method for Estimating the Variance of the Rate of Return. Journal of Business 53, 61–65. Pedersen, R. S. (2015). Inference and testing on the boundary in extended constant correlation GARCH models. Working Paper. Shephard, N. and K. Sheppard (2010). Realising the future: forecasting with high frequency based volatility (HEAVY). Journal of Applied Econometrics 25, 197–231. Straumann, D. and T. Mikosch (2006). QuasiMaximumLikelihood Estimation in Conditionally Heteroscedastic Time Series: A Stochastic Recurrence Equations Approach. The Annals of Statistics 34, 2449–2495. Sucarrat, G. (2015). lgarch: Simulation and estimation of logGARCH models. R package version 0.6. http://cran.rproject.org/web/packages/lgarch/. Sucarrat, G., G. Bjønnes, and S. Grønneberg (2015). Models of Financial Return With TimeVarying Zero Probability. Work in progress. Sucarrat, G. and Á. Escribano (2014). Unbiased Estimation of LogGARCH Models in the Presence of Zero Returns. MPRA Paper No. 59040. http://mpra.ub.unimuenchen. de/59040/. Sucarrat, G., S. Grønneberg, and Á. Escribano (2015). Estimation and Inference in Univariate and Multivariate LogGARCHX Models When the Conditional Density is Unknown. MPRA Paper No. 62352. Online at http://mpra.ub.unimuenchen.de/62352/. An earlier version circulated as “The Power LogGARCH Model", Universidad Carlos III de Madrid Working Paper 1013 in the Economic Series, June 2010. Tauchen, G. and M. Pitts (1983). The Price VariabilityVolume Relationship on Speculative Markets. Econometrica 51, 485–505. Wintenberger, O. (2013). Continuous Invertibility and Stable QML Estimation of the EGARCH(1,1) model. Scandinavian Journal of Statistics 40, 846–867. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/67140 