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Time series properties of ARCH processes with persistent covariates

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  • Han, Heejoon
  • Park, Joon Y.

Abstract

We consider ARCH processes with persistent covariates and provide asymptotic theories that explain how such covariates affect various characteristics of volatility. Specifically, we propose and study a volatility model, named ARCH-NNH model, that is an ARCH(1) process with a nonlinear function of a persistent, integrated or nearly integrated, explanatory variable. Statistical properties of time series given by this model are investigated for various volatility functions. It is shown that our model generates time series that have two prominent characteristics: high degree of volatility persistence and leptokurtosis. Due to persistent covariates, the time series generated by our model has the long memory property in volatility that is commonly observed in high frequency speculative returns. On the other hand, the sample kurtosis of the time series generated by our model either diverges or has a well-defined limiting distribution with support truncated on the left by the kurtosis of the innovation, which successfully explains the empirical finding of leptokurtosis in financial time series. We present two empirical applications of our model. It is shown that the default premium (the yield spread between Baa and Aaa corporate bonds) predicts stock return volatility, and the interest rate differential between two countries accounts for exchange rate return volatility. The forecast evaluation shows that our model generally performs better than GARCH(1,1) and FIGARCH at relatively lower frequencies.

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  • Han, Heejoon & Park, Joon Y., 2006. "Time series properties of ARCH processes with persistent covariates," MPRA Paper 5199, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:5199
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    1. Park, Joon, 2003. "Weak Unit Roots," Working Papers 2003-17, Rice University, Department of Economics.
    2. Kwiatkowski, Denis & Phillips, Peter C. B. & Schmidt, Peter & Shin, Yongcheol, 1992. "Testing the null hypothesis of stationarity against the alternative of a unit root : How sure are we that economic time series have a unit root?," Journal of Econometrics, Elsevier, vol. 54(1-3), pages 159-178.
    3. Hodrick, Robert J., 1989. "Risk, uncertainty, and exchange rates," Journal of Monetary Economics, Elsevier, vol. 23(3), pages 433-459, May.
    4. Granger, Clive W. J. & Hyung, Namwon, 2004. "Occasional structural breaks and long memory with an application to the S&P 500 absolute stock returns," Journal of Empirical Finance, Elsevier, vol. 11(3), pages 399-421, June.
    5. Diebold, Francis X. & Inoue, Atsushi, 2001. "Long memory and regime switching," Journal of Econometrics, Elsevier, vol. 105(1), pages 131-159, November.
    6. Miller, J. Isaac & Park, Joon Y., 2005. "How They Interact to Generate Persistency in Memory," Working Papers 2005-01, Rice University, Department of Economics.
    7. Park, Joon Y & Phillips, Peter C B, 2001. "Nonlinear Regressions with Integrated Time Series," Econometrica, Econometric Society, vol. 69(1), pages 117-161, January.
    8. Schwert, G William, 1989. " Why Does Stock Market Volatility Change over Time?," Journal of Finance, American Finance Association, vol. 44(5), pages 1115-1153, December.
    9. Glosten, Lawrence R & Jagannathan, Ravi & Runkle, David E, 1993. "On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks," Journal of Finance, American Finance Association, vol. 48(5), pages 1779-1801, December.
    10. R. F. Engle & A. J. Patton, 2001. "What good is a volatility model?," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 237-245.
    11. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    12. Park, Joon Y., 2002. "Nonstationary nonlinear heteroskedasticity," Journal of Econometrics, Elsevier, vol. 110(2), pages 383-415, October.
    13. Lamoureux, Christopher G & Lastrapes, William D, 1990. "Heteroskedasticity in Stock Return Data: Volume versus GARCH Effects," Journal of Finance, American Finance Association, vol. 45(1), pages 221-229, March.
    14. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2003. "Modeling and Forecasting Realized Volatility," Econometrica, Econometric Society, vol. 71(2), pages 579-625, March.
    15. Hagiwara, May & Herce, Miguel A, 1999. "Endogenous Exchange Rate Volatility, Trading Volume and Interest Rate Differentials in a Model of Portfolio Selection," Review of International Economics, Wiley Blackwell, vol. 7(2), pages 202-218, May.
    16. Park, Joon Y. & Phillips, Peter C.B., 1999. "Asymptotics For Nonlinear Transformations Of Integrated Time Series," Econometric Theory, Cambridge University Press, vol. 15(3), pages 269-298, June.
    17. Baillie, Richard T. & Bollerslev, Tim & Mikkelsen, Hans Ole, 1996. "Fractionally integrated generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 74(1), pages 3-30, September.
    18. Engle, Robert F. & White (the late), Halbert (ed.), 1999. "Cointegration, Causality, and Forecasting: Festschrift in Honour of Clive W. J. Granger," OUP Catalogue, Oxford University Press, number 9780198296836, Decembrie.
    19. Ding, Zhuanxin & Granger, Clive W. J., 1996. "Modeling volatility persistence of speculative returns: A new approach," Journal of Econometrics, Elsevier, vol. 73(1), pages 185-215, July.
    20. 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.
    21. Weiss, Andrew A., 1986. "Asymptotic Theory for ARCH Models: Estimation and Testing," Econometric Theory, Cambridge University Press, vol. 2(1), pages 107-131, April.
    22. Ding, Zhuanxin & Granger, Clive W. J. & Engle, Robert F., 1993. "A long memory property of stock market returns and a new model," Journal of Empirical Finance, Elsevier, vol. 1(1), pages 83-106, June.
    23. Robinson, Peter M. & Zafaroni, Paolo, 2005. "Pseudo-maximum likelihood estimation of ARCH models," LSE Research Online Documents on Economics 4544, London School of Economics and Political Science, LSE Library.
    24. Chung, Heetaik & Park, Joon Y., 2007. "Nonstationary nonlinear heteroskedasticity in regression," Journal of Econometrics, Elsevier, vol. 137(1), pages 230-259, March.
    25. Gray, Stephen F., 1996. "Modeling the conditional distribution of interest rates as a regime-switching process," Journal of Financial Economics, Elsevier, vol. 42(1), pages 27-62, September.
    26. Diebold, Francis X & Mariano, Roberto S, 2002. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 134-144, January.
    27. Lee, Sang-Won & Hansen, Bruce E., 1994. "Asymptotic Theory for the Garch(1,1) Quasi-Maximum Likelihood Estimator," Econometric Theory, Cambridge University Press, vol. 10(1), pages 29-52, March.
    28. Miller, J. Isaac & Park, Joon Y., 2010. "Nonlinearity, nonstationarity, and thick tails: How they interact to generate persistence in memory," Journal of Econometrics, Elsevier, vol. 155(1), pages 83-89, March.
    29. Lumsdaine, Robin L, 1996. "Consistency and Asymptotic Normality of the Quasi-maximum Likelihood Estimator in IGARCH(1,1) and Covariance Stationary GARCH(1,1) Models," Econometrica, Econometric Society, vol. 64(3), pages 575-596, May.
    30. Thomas Mikosch & Cătălin Stărică, 2004. "Nonstationarities in Financial Time Series, the Long-Range Dependence, and the IGARCH Effects," The Review of Economics and Statistics, MIT Press, vol. 86(1), pages 378-390, February.
    31. Andrews, Donald W K & Monahan, J Christopher, 1992. "An Improved Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimator," Econometrica, Econometric Society, vol. 60(4), pages 953-966, July.
    32. Ser-Huang Poon & Clive W.J. Granger, 2003. "Forecasting Volatility in Financial Markets: A Review," Journal of Economic Literature, American Economic Association, vol. 41(2), pages 478-539, June.
    33. Robinson, Peter M. & Zaffaroni, Paolo, 2005. "Pseudo-maximum likelihood estimation of ARCH(∞) models," LSE Research Online Documents on Economics 58182, London School of Economics and Political Science, LSE Library.
    34. Thomas Mikosch & Catalin Starica, 2004. "Non-stationarities in financial time series, the long range dependence and the IGARCH effects," Econometrics 0412005, University Library of Munich, Germany.
    35. Hillebrand, Eric, 2005. "Neglecting parameter changes in GARCH models," Journal of Econometrics, Elsevier, vol. 129(1-2), pages 121-138.
    36. Nelson, Daniel B., 1990. "Stationarity and Persistence in the GARCH(1,1) Model," Econometric Theory, Cambridge University Press, vol. 6(3), pages 318-334, September.
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    2. 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.
    3. 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.
    4. 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].
    5. 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.
    6. Hu, Shuowen & Poskitt, D.S. & Zhang, Xibin, 2021. "Bayesian estimation for a semiparametric nonlinear volatility model," Economic Modelling, Elsevier, vol. 98(C), pages 361-370.
    7. 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.
    8. Mihaela Craioveanu & Eric Hillebrand, 2012. "Level changes in volatility models," Annals of Finance, Springer, vol. 8(2), pages 277-308, May.
    9. 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.
    10. 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.
    11. Heejoon Han & Shen Zhang, 2012. "Non‐stationary non‐parametric volatility model," Econometrics Journal, Royal Economic Society, vol. 15(2), pages 204-225, June.
    12. 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.
    13. 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.
    14. Hao Sun & Bo Yu, 2020. "Forecasting Financial Returns Volatility: A GARCH-SVR Model," Computational Economics, Springer;Society for Computational Economics, vol. 55(2), pages 451-471, February.

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    More about this item

    Keywords

    ARCH; nonstationarity; nonlinearity; NNH; volatility persistence; leptokurtosis;
    All these keywords.

    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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