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Unobserved Component Models With Asymmetric Conditional Variances

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  • Carmen Broto
  • Esther Ruiz

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Abstract

In this paper, unobserved component models with GARCH disturbances are extended to allow for asymmetric responses of conditional variances to positive and negative shocks. The asymmetric conditional variance is represented by a member of the QARCH class of models. The proposed model allows to distinguish whether the possibly asymmetric conditional heteroscedasticity affects the short run or the long-run disturbances or both. We analyse the statistical properties of the new model and derive the asymptotic and finite sample properties of a QML estimator of the parameters. We propose to identify the conditional heteroscedasticity using the correlogram of the squared auxiliary residuals. Its finite sample properties are also analysed. Finally, we ilustrate the results fitting the model to represent the dynamic evolution of daily series of financial returns and gold prices, as well as of monthly series of inflation. The behaviour of volatility in both types of series is different. The conditional heteroscedasticity mainly affects the short run component in financial returns while in the inflation series, the heteroscedastic ity appears in the long-run component. We find asymmetric effects in both types of variables.

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Paper provided by Universidad Carlos III, Departamento de Estadística y Econometría in its series Statistics and Econometrics Working Papers with number ws032003.

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Date of creation: Nov 2003
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Handle: RePEc:cte:wsrepe:ws032003
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  1. Morgan, I G & Trevor, R G, 1999. "Limit Moves as Censored Observations of Equilibrium Futures Price in GARCH Processes," Journal of Business & Economic Statistics, American Statistical Association, vol. 17(4), pages 397-408, October.
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  13. Ana Pérez & Esther Ruiz, 2003. "Properties of the Sample Autocorrelations of Nonlinear Transformations in Long-Memory Stochastic Volatility Models," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 1(3), pages 420-444.
  14. Sentana,E., 1995. "Quadratic Arch Models," Papers 9517, Centro de Estudios Monetarios Y Financieros-.
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  25. Julio Rodríguez & Esther Ruiz, 2003. "A Powerful Test For Conditional Heteroscedasticity For Financial Time Series With Highly Persistent Volatilities," Statistics and Econometrics Working Papers ws036716, Universidad Carlos III, Departamento de Estadística y Econometría.
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Cited by:

  1. Broto Carmen & Ruiz Esther, 2009. "Testing for Conditional Heteroscedasticity in the Components of Inflation," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 13(2), pages 1-30, May.
  2. Sentana, Enrique & Calzolari, Giorgio & Fiorentini, Gabriele, 2008. "Indirect estimation of large conditionally heteroskedastic factor models, with an application to the Dow 30 stocks," Journal of Econometrics, Elsevier, vol. 146(1), pages 10-25, September.
  3. Haas, Markus & Mittnik, Stefan & Paolella, Marc S., 2008. "Asymmetric multivariate normal mixture GARCH," CFS Working Paper Series 2008/07, Center for Financial Studies (CFS).
  4. Chen, Cathy W.S. & Gerlach, Richard & Lin, Edward M.H., 2008. "Volatility forecasting using threshold heteroskedastic models of the intra-day range," Computational Statistics & Data Analysis, Elsevier, vol. 52(6), pages 2990-3010, February.
  5. repec:dgr:uvatin:2010017 is not listed on IDEAS
  6. Ane, Thierry, 2006. "An analysis of the flexibility of Asymmetric Power GARCH models," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 1293-1311, November.
  7. Broto, Carmen, 2011. "Inflation targeting in Latin America: Empirical analysis using GARCH models," Economic Modelling, Elsevier, vol. 28(3), pages 1424-1434, May.
  8. Pellegrini, Santiago & Ruiz, Esther & Espasa, Antoni, 2010. "Conditionally heteroscedastic unobserved component models and their reduced form," Economics Letters, Elsevier, vol. 107(2), pages 88-90, May.

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