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A tobit model with garch errors

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  • Giorgio Calzolari
  • Gabriele Fiorentini

Abstract

In the context of time series regression, we extend the standard Tobit model to allow for the possibility of conditional heteroskedastic error processes of the GARCH type. We discuss the likelihood function of the Tobit model in the presence of conditionally heteroskedastic errors. Expressing the exact likelihood function turns out to be infeasible, and we propose an approximation by treating the model as being conditionally Gaussian. The performance of the estimator is investigated by means of Monte Carlo simulations. We find that, when the error terms follow a GARCH process, the proposed estimator considerably outperforms the standard Tobit quasi maximum likelihood estimator. The efficiency loss due to the approximation of the likelihood is finally evaluated.

Suggested Citation

  • Giorgio Calzolari & Gabriele Fiorentini, 1998. "A tobit model with garch errors," Econometric Reviews, Taylor & Francis Journals, vol. 17(1), pages 85-104.
    • Handle: RePEc:taf:emetrv:v:17:y:1998:i:1:p:85-104
    DOI: 10.1080/07474939808800404
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    Cited by:

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    2. Juan J. Echavarría & Luis F. Melo-Velandia & Mauricio Villamizar-Villegas, 2018. "The impact of pre-announced day-to-day interventions on the Colombian exchange rate," Empirical Economics, Springer, vol. 55(3), pages 1319-1336, November.
    3. Imane El Ouadghiri & Remzi Uctum, 2015. "Jumps in Equilibrium Prices and Asymmetric News in Foreign Exchange Markets," Working Papers hal-04141414, HAL.
    4. Giot, Pierre & Laurent, Sébastien & Petitjean, Mikael, 2010. "Trading activity, realized volatility and jumps," Journal of Empirical Finance, Elsevier, vol. 17(1), pages 168-175, January.
    5. Dimitrakopoulos, Stefanos & Tsionas, Mike, 2019. "Ordinal-response GARCH models for transaction data: A forecasting exercise," International Journal of Forecasting, Elsevier, vol. 35(4), pages 1273-1287.
    6. Zhao, Wandi & Gao, Yang & Wang, Mingjin, 2022. "Measuring liquidity with return volatility: An analytical approach based on heavy-tailed Censored-GARCH model," The North American Journal of Economics and Finance, Elsevier, vol. 62(C).
    7. Hsieh, Ping-Hung & Yang, J. Jimmy, 2009. "A censored stochastic volatility approach to the estimation of price limit moves," Journal of Empirical Finance, Elsevier, vol. 16(2), pages 337-351, March.
    8. Slim, Skander & Dahmene, Meriam, 2016. "Asymmetric information, volatility components and the volume–volatility relationship for the CAC40 stocks," Global Finance Journal, Elsevier, vol. 29(C), pages 70-84.
    9. 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.
    10. Boffelli, Simona & Urga, Giovanni, 2015. "Macroannouncements, bond auctions and rating actions in the European government bond spreads," Journal of International Money and Finance, Elsevier, vol. 53(C), pages 148-173.
    11. Chen, Ho-Chyuan & Chang, Kuang-Liang & Yu, Shih-Ti, 2012. "Application of the Tobit model with autoregressive conditional heteroscedasticity for foreign exchange market interventions," Japan and the World Economy, Elsevier, vol. 24(4), pages 274-282.
    12. Calzolari, Giorgio & Fiorentini, Gabriele, 1993. "Estimating variances and covariances in a censored regression model," MPRA Paper 22598, University Library of Munich, Germany, revised 1993.

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    More about this item

    Keywords

    censored regressions; conditional heteroskedasticity; Monte Carlo simulations;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C24 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Truncated and Censored Models; Switching Regression Models; Threshold Regression Models

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