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Time series properties of ARCH processes with persistent covariates

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Author Info
Han, Heejoon
Park, Joon Y.

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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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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 5199.

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Date of creation: May 2006
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Handle: RePEc:pra:mprapa:5199

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Related research
Keywords: ARCH; nonstationarity; nonlinearity; NNH; volatility persistence; leptokurtosis;

Find related papers by JEL classification:
C50 - Mathematical and Quantitative Methods - - Econometric Modeling - - - General
G12 - Financial Economics - - General Financial Markets - - - Asset Pricing
C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions

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    Other versions:
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    Other versions:
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  16. 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. [Downloadable!] (restricted)
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  17. 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.
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  21. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April. [Downloadable!] (restricted)
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  23. Park, Joon Y., 2002. "Nonstationary nonlinear heteroskedasticity," Journal of Econometrics, Elsevier, vol. 110(2), pages 383-415, October. [Downloadable!] (restricted)
  24. 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. [Downloadable!] (restricted)
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  25. 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, 01. [Downloadable!] (restricted)
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