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Unobserved component models with asymmetric conditional variances

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  • Broto, Carmen
  • Ruiz, Esther

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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Bibliographic Info

Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

Volume (Year): 50 (2006)
Issue (Month): 9 (May)
Pages: 2146-2166

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Handle: RePEc:eee:csdana:v:50:y:2006:i:9:p:2146-2166

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References

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  1. Sentana, Enrique, 1995. "Quadratic ARCH Models," Review of Economic Studies, Wiley Blackwell, vol. 62(4), pages 639-61, October.
  2. Enrique Sentana & Giorgio Calzolari & Gabriele Fiorentini, 2004. "Indirect Estimation Of Conditionally Heteroskedastic Factor Models," Working Papers wp2004_0409, CEMFI.
  3. Gabriele Fiorentini & Enrique Sentana & Neil Shephard, 2002. "Likelihood-based estimation of latent generalised ARCH structures," Economics Papers 2002-W19, Economics Group, Nuffield College, University of Oxford.
  4. 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.
  5. Ord, J.K. & Koehler, A. & Snyder, R.D., 1995. "Estimation and Prediction for a Class of Dynamic Nonlinear Statistical Models," Monash Econometrics and Business Statistics Working Papers 4/95, Monash University, Department of Econometrics and Business Statistics.
  6. Harvey, Andrew & Ruiz, Esther & Sentana, Enrique, 1992. "Unobserved component time series models with Arch disturbances," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 129-157.
  7. Allan D. Brunner & Gregory D. Hess, 1990. "Are higher levels of inflation less predictable? A state-dependent conditional heteroskedasticity approach," Finance and Economics Discussion Series 141, Board of Governors of the Federal Reserve System (U.S.).
  8. Charles S. Bos & Ronald J. Mahieu & Herman K. van Dijk, 2001. "On the Variation of Hedging Decisions in Daily Currency Risk Management," Tinbergen Institute Discussion Papers 01-018/4, Tinbergen Institute.
  9. Maravall, Agustin, 1987. "Minimum Mean Squared Error Estimation of the Noise in Unobserved Component Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 5(1), pages 115-20, January.
  10. Martin Evans & Paul Wachtel, 1993. "Inflation regimes and the sources of inflation uncertainty," Proceedings, Federal Reserve Bank of Cleveland, pages 475-520.
  11. Giorgio Calzolari & Gabriele Fiorentini & Enrique Sentana, 2004. "Constrained Indirect Estimation," Review of Economic Studies, Wiley Blackwell, vol. 71(4), pages 945-973, October.
  12. 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.
  13. Mervyn King & Enrique Sentana & Sushil Wadhwani, 1990. "Volatiltiy and Links Between National Stock Markets," NBER Working Papers 3357, National Bureau of Economic Research, Inc.
  14. Durbin, James & Koopman, Siem Jan, 2001. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, number 9780198523543.
  15. He, Changli & Terasvirta, Timo, 1999. "Properties of moments of a family of GARCH processes," Journal of Econometrics, Elsevier, vol. 92(1), pages 173-192, September.
  16. Wei, Steven X., 2002. "A censored-GARCH model of asset returns with price limits," Journal of Empirical Finance, Elsevier, vol. 9(2), pages 197-223, March.
  17. Mardi Dungey & Vance L Martin & Adrian R Pagan, 2000. "A multivariate latent factor decomposition of international bond yield spreads," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 15(6), pages 697-715.
  18. Koopman S.J. & Bos C.S., 2004. "State Space Models With a Common Stochastic Variance," Journal of Business & Economic Statistics, American Statistical Association, vol. 22, pages 346-357, July.
  19. Evans, Martin, 1991. "Discovering the Link between Inflation Rates and Inflation Uncertainty," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 23(2), pages 169-84, May.
  20. Maravall, Agustin, 1983. "An Application of Nonlinear Time Series Forecasting," Journal of Business & Economic Statistics, American Statistical Association, vol. 1(1), pages 66-74, January.
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Citations

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Cited by:
  1. 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.
  2. Broto, Carmen, 2011. "Inflation targeting in Latin America: Empirical analysis using GARCH models," Economic Modelling, Elsevier, vol. 28(3), pages 1424-1434, May.
  3. Carmen Broto & Esther Ruiz, 2008. "Testing for conditional heteroscedasticity in the components of inflation," Banco de Espa�a Working Papers 0812, Banco de Espa�a.
  4. Gabriele Fiorentini & Giorgio Calzolari & Enrique Sentana, 2007. "Indirect estimation of large conditionally heteroskedastic factor models, with an application to the Dow 30 stocks," Working Paper Series 40-07, The Rimini Centre for Economic Analysis, revised Jul 2007.
  5. 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.
  6. Haas, Markus & Mittnik, Stefan & Paolella, Marc S., 2008. "Asymmetric multivariate normal mixture GARCH," CFS Working Paper Series 2008/07, Center for Financial Studies (CFS).
  7. Charles S. Bos & Siem Jan Koopman, 2010. "Models with Time-varying Mean and Variance: A Robust Analysis of U.S. Industrial Production," Tinbergen Institute Discussion Papers 10-017/4, Tinbergen Institute.

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