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Time series properties of ARCH processes with persistent covariates

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  • Han, Heejoon
  • Park, Joon Y.

Abstract

We investigate the time series properties of a volatility model, whose conditional variance is specified as in ARCH with an additional persistent covariate. The included covariate is assumed to be an integrated or nearly integrated process, with its effect on volatility given by a wide class of nonlinear volatility functions. In the paper, such a model is shown to generate many important characteristics that are commonly observed in financial time series. In particular, the model yields persistence in volatility, and also well predicts leptokurtosis. This is true for any type of volatility functions considered in the paper, as long as the covariate is integrated or nearly integrated. Stationary covariates cannot produce important characteristics observed in many financial time series. We present two empirical applications of the model, which show that the default premium (the yield spread between Baa and Aaa corporate bonds) affects stock return volatility and the interest rate differential between two countries accounts for exchange rate return volatility. The forecast evaluation shows that the model generally outperforms GARCH and FIGARCH at relatively lower frequencies.

Suggested Citation

  • Han, Heejoon & Park, Joon Y., 2008. "Time series properties of ARCH processes with persistent covariates," Journal of Econometrics, Elsevier, vol. 146(2), pages 275-292, October.
  • Handle: RePEc:eee:econom:v:146:y:2008:i:2:p:275-292
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    Cited by:

    1. Christensen, Bent Jesper & Dahl, Christian M. & Iglesias, Emma M., 2012. "Semiparametric inference in a GARCH-in-mean model," Journal of Econometrics, Elsevier, vol. 167(2), pages 458-472.
    2. Leandro Maciel & Fernando Gomide & Rosangela Ballini, 2014. "An Evolving Fuzzy-Garch Approach Forfinancial Volatility Modeling And Forecasting," Anais do XL Encontro Nacional de Economia [Proceedings of the 40th Brazilian Economics Meeting] 138, ANPEC - Associação Nacional dos Centros de Pós-Graduação em Economia [Brazilian Association of Graduate Programs in Economics].
    3. Jawadi, Fredj & Louhichi, Waël & Ameur, Hachmi Ben & Cheffou, Abdoulkarim Idi, 2016. "On oil-US exchange rate volatility relationships: An intraday analysis," Economic Modelling, Elsevier, vol. 59(C), pages 329-334.
    4. Heejoon Han & Myung D. Park, 2013. "Comparison of Realized Measure and Implied Volatility in Forecasting Volatility," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 32(6), pages 522-533, September.
    5. Mihaela Craioveanu & Eric Hillebrand, 2012. "Level changes in volatility models," Annals of Finance, Springer, vol. 8(2), pages 277-308, May.
    6. Ming Chen & Qiongxia Song, 2016. "Semi-parametric estimation and forecasting for exogenous log-GARCH models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(1), pages 93-112, March.
    7. Han, Heejoon & Park, Joon Y., 2012. "ARCH/GARCH with persistent covariate: Asymptotic theory of MLE," Journal of Econometrics, Elsevier, vol. 167(1), pages 95-112.
    8. Louhichi, Waël, 2011. "What drives the volume-volatility relationship on Euronext Paris?," International Review of Financial Analysis, Elsevier, vol. 20(4), pages 200-206, August.
    9. Heejoon Han & Shen Zhang, 2012. "Non‐stationary non‐parametric volatility model," Econometrics Journal, Royal Economic Society, vol. 15(2), pages 204-225, June.
    10. Leandro Maciel, 2012. "A Hybrid Fuzzy GJR-GARCH Modeling Approach for Stock Market Volatility Forecasting," Brazilian Review of Finance, Brazilian Society of Finance, vol. 10(3), pages 337-367.
    11. Leandro Maciel & Fernando Gomide & Rosangela Ballini, 2016. "Evolving Fuzzy-GARCH Approach for Financial Volatility Modeling and Forecasting," Computational Economics, Springer;Society for Computational Economics, vol. 48(3), pages 379-398, October.

    More about this item

    Keywords

    ARCH Persistent covariate Nonstationarity Nonlinearity Volatility persistence Leptokurtosis;

    JEL classification:

    • C50 - Mathematical and Quantitative Methods - - Econometric Modeling - - - General
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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