Han, Heejoon and Park, Joon Y. (2006): Time series properties of ARCH processes with persistent covariates.

PDF
MPRA_paper_5199.pdf Download (392kB)  Preview 
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 ARCHNNH 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 welldefined 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.
Item Type:  MPRA Paper 

Original Title:  Time series properties of ARCH processes with persistent covariates 
Language:  English 
Keywords:  ARCH; nonstationarity; nonlinearity; NNH; volatility persistence; leptokurtosis 
Subjects:  C  Mathematical and Quantitative Methods > C5  Econometric Modeling > C50  General G  Financial Economics > G1  General Financial Markets > G12  Asset Pricing ; Trading Volume ; Bond Interest Rates C  Mathematical and Quantitative Methods > C2  Single Equation Models ; Single Variables > C22  TimeSeries Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes 
Item ID:  5199 
Depositing User:  Heejoon Han 
Date Deposited:  08. Oct 2007 
Last Modified:  04. Jun 2015 13:35 
References:  Andersen, T.G., Bollerslev, T., Diebold, F.X. and Labys, P. (2003), "Modeling and forecasting realized volatility," Econometrica, 71, 529626. Andrews, D.W.K. and Monahan, J. (1992), "An improved heteroskedasticity and autocorrelation consistent covariance matrix estimator," Econometrica, 60, 953966. Baillie, R.T., Bollerslev, T., and Mikkelsen, H.O. (1996), "Fractionally integrated generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, 74, 330. Bartlett, M.S. (1946), "On the theoretical specification of sampling properties of autocorrelated time series," Journal of the Royal Statistical Society, B 8, 2441. Berkes, L., Horvath, L., and Kokoszka, P. (2003): "GARCH processes: structure and estimation," Bernoulli, 9, 201207. Bollerslev, T. (1986), "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, 31, 307327. Bollerslev, T., Engle, R.F., and Nelson, D.B. (1994): "ARCH models," In R.F. Engle and D.L. McFadden, eds., Handbook of Econometrics, Vol. 4, 29593038, Elsevier: Amsterdam. Bollerslev, T. and Wooldridge, J.M. (1992), "Quasimaximum likelihood estimation and inference in dynamic models with timevarying covariances," Econometric reviews, 11, 143172. Chung, H. and Park, J.Y. (2004), "Nonstationary nonlinear heteroskedasticity in regression," mimeograph, Department of Economics, Rice University. Ding, Z. and Granger, C.W.J. (1996), "Modeling volatility persistence of speculative returns: A new approach," Journal of Econometrics, 73, 185215. Ding, Z., Granger, C.W.J., and Engle, R.F. (1993), "A long memory property of stock market returns and a new model," Journal of Empirical Finance, 1, 83106. Diebold, F.X. and Mariano, R.S. (1995), "Comparing predictive accuracy," Journal of Business and Economic Statistics, 13, 253263. Diebold, F.X. and Inoue, A. (2001), "Long memory and regime switching," Journal of Econometrics, 105, 131159. Engle, R.F. (1982), "Autoregressive conditional heteroskedasticity with estimates of the variance of U.K. Inflation," Econometrica, 50, 9871008. Engle, R.F. and Lee, G.J. (1999), A longrun and shortrun component model of stock return volatility, in Engle R. and H. White ed. Cointegration, Causality, and Forecasting: A Festschrift in Honour of Clive W.J. Granger, Chapter 10, 475497, Oxford University Press. Engle, R.F. and Patton, A.J. (2001), "What good is a volatility model?," Quantitative Finance, 1(2), 237245. Glosten, L.R., Jagannathan, R. and Runkle, D. (1993), "On the relation between the expected value and the volatility of nominal excess returns on stocks," Journal of Finance, 48, 17791801. Granger, C.W.J. and Hyung, N. (2004), "Occasional structural breaks and long memory with an application to the S&P 500 absolute stock returns," Journal of Empirical Finance, 11, 399421. Gray, S.F. (1996), "Modeling the conditional distribution of interest rates as a regimeswitching process," Journal of Financial Economics, 42, 2762. He, C. and Teräsvirta, T. (1999), "Properties of moments of a family of GARCH processes," Journal of Econometrics, 92, 173192. Hagiwara, M. and Herce, M.A. (1999), "Endogenous exchange rate volatility, trading volume and interest rate differentials in a model of portfolio selection," Review of International Economics, 7(2), 202218. Han, H. and Park, J.Y. (2006), "ARCH models with persistent covariates: asymptotic distribution theory of QMLE and IGARCH behavior," mimeograph, Department of Economics, National University of Singapore. Hillebrand, E. (2005), "Neglecting parameter changes in GARCH models," Journal of Econometrics, 129, 121138. Hodrick R.J. (1989), "Risk, uncertainty, and exchange rates," Journal of Monetary Economics, 23, 433459. Hol, E.M.J.H. (2003), Empirical studies on volatility in international stock markets. Dordrecht: Kluwer Academic. Hyung, N., Poon, S.H. and Granger, C.W.J. (2006), "A source of long memory in volatility," mimeograph, Manchester Business School, University of Manchester. Kwiatkowski, D., Phillips, P.C.B., Schmidt, P. and Shin, Y. (1992), "Testing the null hypothesis of stationarity against the alternative of a unit root," Journal of Econometrics, 54, 159178. Lamoureux, C.G. and Lastrapes, W.D. (1990), "Heteroskedasticity in stock return data: volume versus GARCH effects," Journal of Finance, 45, 221229. Laurent, S. and Peters, J.P. (2005), "G@RCH 4.0, Estimating and forecasting ARCH models," Timberlake Consultants. Lee, S.W. and Hansen, B.E. (1994), "Asymptotic theory for the GARCH(1,1) quasimaximum likelihood estimator," Econometric Theory, 10, 2952. Lumsdaine, R.L. (1996), "Consistency and asymptotic normality of the quasimaximum likelihood estimator in IGARCH(1,1) and covariance stationary GARCH(1,1) models," Econometrica, 64, 575596. Mikosch, T. and Starica, C. (2004), "Nonstationarities in financial time series, the longrange dependence, and the IGARCH effects," The Review of Economics and Statistics, 86, 378390. Miller, J.I. and Park, J.Y. (2005), "Nonlinearity, nonstationarity, and thick tails: how they interact to generate persistence in memory," mimeograph, Department of Economics, Rice University. Nelson, D.B. (1990), "Stationarity and persistence in the GARCH(1,1,) model," Econometric Theory, 6, 318334. Park, J.Y. (2002), "Nonstationary nonlinear heteroskedasticity," Journal of Econometrics, 110, 383415. Park, J.Y. (2003), "Weak unit root," mimeograph, Department of Economics, Rice University. Park, J.Y. and Phillips, P.C.B. (1999), "Asymptotics for nonlinear transformations of integrated time series," Econometric Theory, 15, 269298. Park, J.Y. and Phillips, P.C.B. (2001), "Nonlinear regressions with integrated time series," Econometrica, 69, 117161. Phillips, P.C.B. (1987), "Towards a unified asymptotic theory for autoregression," Biometrika, 74, 535547. Phillips, P.C.B. and Perron, P. (1988), "Testing for a unit root in time series regression," Biometrika, 75, 335346. Poon, S.H. and Granger, C.W.J. (2003), "Forecasting volatility in financial markets," Journal of Economic Literature, 41, 478539. Robinson, P.M. and Zaffaroni, P. (2005), "Pseudomaximum likelihood estimation of ARCH(∞) models," Annals of Statistics, forthcoming. Schwert, G.W. (1989), "Why does stock market volatility change over time?," Journal of Finance, 44, 11151154. Stock, J.H. (1994): "Unit roots and structural breaks," In R.F. Engle and D.L. McFadden, eds., Handbook of Econometrics, Vol. 4, 27392841, Elsevier: Amsterdam. Weiss, A. (1986), "Asymptotic theory for ARCH models," Econometric Theory, 2, 107131. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/5199 