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Unobserved component models with asymmetric conditional variances

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Listed author(s):
  • Ruiz, Esther
  • Broto, Carmen

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 de Madrid. Departamento de Estadística in its series DES - Working Papers. Statistics and Econometrics. WS with number ws032003.

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Date of creation: Nov 2003
Handle: RePEc:cte:wsrepe:ws032003
Contact details of provider: Web page: http://portal.uc3m.es/portal/page/portal/dpto_estadistica

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  1. Gabriele Fiorentini & Enrique Sentana & Neil Shephard, 2004. "Likelihood-Based Estimation of Latent Generalized ARCH Structures," Econometrica, Econometric Society, vol. 72(5), pages 1481-1517, 09.
  2. Enrique Sentana & Giorgio Calzolari & Gabriele Fiorentini, 2004. "Indirect Estimation Of Conditionally Heteroskedastic Factor Models," Working Papers wp2004_0409, CEMFI.
  3. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-370, March.
  4. Brunner, Allan D & Hess, Gregory D, 1993. "Are Higher Levels of Inflation Less Predictable? A State-Dependent Conditional Heteroscedasticity Approach," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(2), pages 187-197, April.
  5. Martin Evans & Paul Wachtel, 1993. "Inflation regimes and the sources of inflation uncertainty," Proceedings, Federal Reserve Bank of Cleveland, pages 475-520.
  6. Bos, C.S. & Mahieu, R.J. & van Dijk, H.K., 2000. "On the variation of hedging decisions in daily currency risk management," Econometric Institute Research Papers EI 2000-20/A, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
  7. Evans, Martin, 1991. "Discovering the Link between Inflation Rates and Inflation Uncertainty," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 23(2), pages 169-184, May.
  8. Harvey, Andrew C & Koopman, Siem Jan, 1992. "Diagnostic Checking of Unobserved-Components Time Series Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(4), pages 377-389, October.
  9. Durbin, James & Koopman, Siem Jan, 2012. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, edition 2, number 9780199641178, April.
  10. 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.
  11. Ruiz, Esther & Rodríguez, Julio, 2003. "A powerful test for conditional heteroscedasticity for financial time series with highly persistent volatilities," DES - Working Papers. Statistics and Econometrics. WS ws036716, Universidad Carlos III de Madrid. Departamento de Estadística.
  12. 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.
  13. 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.
  14. 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.
  15. 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.
  16. 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.
  17. Kim, Chang-Jin, 1993. "Unobserved-Component Time Series Models with Markov-Switching Heteroscedasticity: Changes in Regime and the Link between Inflation Rates and Inflation Uncertainty," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(3), pages 341-349, July.
  18. 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 115-120, January.
  19. King, Mervyn & Sentana, Enrique & Wadhwani, Sushil, 1994. "Volatility and Links between National Stock Markets," Econometrica, Econometric Society, vol. 62(4), pages 901-933, July.
  20. 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.
  21. Enrique Sentana, 1995. "Quadratic ARCH Models," Review of Economic Studies, Oxford University Press, vol. 62(4), pages 639-661.
  22. 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.
  23. 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.
  24. Giorgio Calzolari & Gabriele Fiorentini & Enrique Sentana, 2004. "Constrained Indirect Estimation," Review of Economic Studies, Oxford University Press, vol. 71(4), pages 945-973.
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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. Haas, Markus & Mittnik, Stefan & Paolella, Marc S., 2009. "Asymmetric multivariate normal mixture GARCH," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2129-2154, April.
  3. Broto, Carmen, 2011. "Inflation targeting in Latin America: Empirical analysis using GARCH models," Economic Modelling, Elsevier, vol. 28(3), pages 1424-1434, May.
  4. 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.
  5. 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.
  6. 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.
  7. 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.
  8. repec:rim:rimwps:40-07 is not listed on IDEAS
  9. 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.

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