References Bollerslev, T. (1986), Generalised autoregressive conditional heteroscedasticity, Journal of Econometrics, 31, 307-327. Boussama, F. (2000), Asymptotic normality for the quasi-maximum likelihood estimator of a GARCH model, Comptes Rendus de l’Academie des Sciences, Serie I, 331, 81-84 (in French). Chan, F., C. Lim and M. McAleer (2005), Modelling multivariate international tourism demand and volatility, Tourism Management, 26, 459-471. Corsi, F. (2004), A simple long memory model of realized volatility," Unpublished paper, University of Southern Switzerland. Dickey, D.A. and W.A. Fuller (1979), Distribution of the estimators for autoregressive time series with a unit root, Journal of the American Statistical Association, 74, 427-431. Dickey, D.A. and W.A. Fuller (1981), Likelihood ratio statistics for autoregressive time series with a unit root, Econometrica, 49, 1057-1072. Divino, J.A. and M. McAleer (2008), Modelling and forecasting sustainable international tourism demand for the Brazilian Amazon, to appear in Environmental Modelling & Software. Elie, L. and T. Jeantheau (1995), Consistency in heteroskedastic models, Comptes Rendus de l’Académie des Sciences, Série I, 320, 1255-1258 (in French). Engle, R.F. (1982), Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation, Econometrica, 50, 987-1007. Glosten, L., R. Jagannathan and D. Runkle (1992), On the relation between the expected value and volatility of nominal excess return on stocks, Journal of Finance, 46, 1779-1801. Hoti, S., M. McAleer and R. Shareef (2005), Modelling country risk and uncertainty in small island tourism economies, Tourism Economics, 11, 159-183. Hoti, S., M. McAleer and R. Shareef (2007), Modelling international tourism and country risk spillovers for Cyprus and Malta, Tourism Management, 28, 1472-84. Jeantheau, T. (1998), Strong consistency of estimators for multivariate ARCH models, Econometric Theory, 14, 70-86. Lee, S.W. and B.E. Hansen (1994), Asymptotic theory for the GARCH(1,1) quasi-maximum likelihood estimator, Econometric Theory, 10, 29-52. Li, W.K., S. Ling and M. McAleer (2002), Recent theoretical results for time series models with GARCH errors, Journal of Economic Surveys, 16, 245-269. Reprinted in M. McAleer and L. Oxley (eds.), Contributions to Financial Econometrics: Theoretical and Practical Issues, Blackwell, Oxford, 2002, pp. 9-33. Ling, S. and W.K. Li (1997), On fractionally integrated autoregressive moving-average models with conditional heteroskedasticity, Journal of the American Statistical Association, 92, 1184-1194. Ling, S. and M. McAleer (2002a), Stationarity and the existence of moments of a family of GARCH processes, Journal of Econometrics, 106, 109-117. Ling, S. and M. McAleer (2002b), Necessary and sufficient moment conditions for the GARCH(r,s) and asymmetric power GARCH(r,s) models, Econometric Theory, 18, 722-729. Ling, S. and M. McAleer, (2003a), Asymptotic theory for a vector ARMA-GARCH model, Econometric Theory, 19, 278-308. Ling, S. and M. McAleer (2003b), On adaptive estimation in nonstationary ARMA models with GARCH errors, Annals of Statistics, 31, 642-674. McAleer, M. (2005), Automated inference and learning in modeling financial volatility, Econometric Theory, 21, 232-261. McAleer, M. (2009), The Ten Commandments for optimizing value-at-risk and daily capital charges, to appear in journal of Economic Surveys. McAleer, M., F. Chan and D. Marinova (2007), An econometric analysis of asymmetric volatility: theory and application to patents, Journal of Econometrics, 139, 259-284. McAleer, M. and J.A. Divino (2008), Modelling the growth and volatility in daily international mass tourism to Peru, unpublished paper, Department of Economics, Catholic University of Brasilia, Brazil. McAleer, M. and M. Medeiros (2008), A multiple regime smooth transition heterogeneous autoregressive model for long memory and asymmetries, Journal of Econometrics, 147(1), 2008, 104-119. McAleer, M and B. da Veiga (2008a), Forecasting value-at-risk with a parsimonious portfolio spillover GARCH (PS-GARCH) model, Journal of Forecasting, 27, 1-19. McAleer, M and B. da Veiga (2008b), Single-index and portfolio models for forecasting value-atrisk thresholds, Journal of Forecasting, 27, 217-235. Muller, U., M. Dacorogna, R. Dav, R. Olsen, O. Pictet and J. ward (1993), Fractals and intrinsic time - a challenge to econometricians," in Proceedings of the XXXIXth International AEA Conference on Real Time Econometrics. Nelson, D.B. (1991), Conditional heteroscedasticity in asset returns: a new approach, Econometrica, 59, 347-370. Phillips, P.C.B. and P. Perron (1988), Testing for a unit root in time series regression, Biometrika, 75, 335-346. Shareef, R. and M. McAleer (2005), Modelling international tourism demand and volatility in small island tourism economies, International Journal of Tourism Research, 7, 313-333. Shareef, R. and M. McAleer (2007), Modelling the uncertainty in international tourist arrivals to the Maldives, Tourism Management, 28, 23-45. Shareef, R. and M. McAleer (2008), Modelling international tourism demand and uncertainty in Maldives and Seychelles: a portfolio approach, Mathematics and Computers in Simulation, 78, 459-68. Shephard, N. (1996), Statistical aspects of ARCH and stochastic volatility, in O.E. BarndorffNielsen, D.R. Cox and D.V. Hinkley (eds.), Statistical Models in Econometrics, Finance and Other Fields, Chapman & Hall, London, pp. 1-67.