Asymptotic Theory for the QMLE in GARCH-X Models With Stationary and Nonstationary Covariates

REFERENCES

• Barndorff-Nielsen, O.E., and Shephard, N. (2007), “Variation, Jumps and High Frequency Data in Financial Econometrics,” in Advances in Economics and Econometrics. Theory and Applications, Ninth World Congress, eds. R. Blundell, T. Persson, and W. K. Newey, Econometric Society Monographs, Cambridge, UK: Cambridge University Press, pp. 328–372.
   Google Scholar
• Berkes, I., Horváth, L., and Kokoszka, P. (2003), “GARCH Processes: Structure and Estimation,” Bernoulli, 9, 201–227.
   Web of Science ®Google Scholar
• Billingsley, P. (1974), “Conditional Distributions and Tightness,” Annals of Probability, 2, 480–485.
   Web of Science ®Google Scholar
• Bollerslev, T. (1986), “Generalized Autoregressive Conditional Heteroskedasticity,” Journal of Econometrics, 31, 307–327.
   Web of Science ®Google Scholar
• Bollerslev, T., and Melvin, M. (1994), “Bid-Ask Spreads and the Volatility in the Foreign Exchange Market: An Empirical Analysis,” Journal of International Economics, 36, 355–372.
   Web of Science ®Google Scholar
• Brenner, R.J., Harjes, R.H., and Kroner, K.F. (1996), “Another Look at Models of the Short-Term Interest Rate,” Journal of Financial and Quantitative Analysis, 31, 85–107.
   Web of Science ®Google Scholar
• Brown, B. (1971), “Martingale Central Limit Theorems,” Annals of Mathematical Statistics, 42, 59–66.
   Google Scholar
• Carrasco, M., and Chen, X. (2002), “Mixing and Moment Properties of Various GARCH and Stochastic Volatility Models,” Econometric Theory, 18, 17–39.
   Web of Science ®Google Scholar
• Dittmann, I., and Granger, C. W.J. (2002), “Properties of Nonlinear Transformations of Fractionally Integrated Processes,” Journal of Econometrics, 110, 113–133.
   Web of Science ®Google Scholar
• Dominguez, K. (1998), “Central Bank Intervention and Exchange Rate Volatility,” Journal of International Money and Finance, 17, 161–190.
   Web of Science ®Google Scholar
• Engle, R.F. (2002), “New Frontiers for ARCH Models,” Journal of Applied Econometrics, 17, 425–446.
   Web of Science ®Google Scholar
• Engle, R.F., and Gallo, G.M. (2006), “A Multiple Indicators Model for Volatility Using Intra-Daily Data,” Journal of Econometrics, 131, 3–27.
   Web of Science ®Google Scholar
• Escanciano, J.M. (2009), “Quasi-Maximum Likelihood Estimation of Semi-Strong GARCH Models,” Econometric Theory, 25, 561–570.
   Web of Science ®Google Scholar
• Fleming, J., Kirby, C., and Ostdiek, B. (2008), “The Specification of GARCH Models With Stochastic Covariates,” Journal of Futures Markets, 28, 911–934.
   Web of Science ®Google Scholar
• Franq, C., and Zakoïan, J.-M. (2012), “Strict Stationarity Testing and Estimation of Explosive and Stationary Generalized Autoregressive Conditional Heteroskedasticity Models,” Econometrica, 80, 821–861.
   Web of Science ®Google Scholar
• Gallo, G., and Pacini, B. (2000), “The Effects of Trading Activity on Market Volatility,” European Journal of Finance, 6, 163–175.
   Google Scholar
• Girma, P., and Mougoue, M. (2002), “An Empirical Examination of the Relation Between Futures Spreads Volatility, Volume, and Open Interest,” Journal of Futures Markets, 22, 1083–1102.
   Web of Science ®Google Scholar
• Glosten, L. R., Jagannathan, R., and Runkle, D. (1983), “On the Relation Between the Expected Value and the Volatility of the Nominal Excess Return on Stocks,” Journal of Finance, 48, 1779–1801.
   Google Scholar
• Gray, S. F. (1996), “Modeling the Conditional Distribution of Interest Rates as a Regime-Switching Process,” Journal of Financial Economics, 42, 27–62.
   Web of Science ®Google Scholar
• Hagiwara, M., and Herce, M. (1999), “Endogenous Exchange Rate Volatility, Trading Volume and Interest Rate Differentials in a Model of Portfolio Selection,” Review of International Economics, 7, 202–218.
   Google Scholar
• Hall, P., and Heyde, C.C. (1980), Martingale Limit Theory and Its Application, New York: Academic Press.
   Google Scholar
• Han, H. (2014), “Asymptotic Properties of GARCH-X Processes,” forthcoming in Journal of Financial Econometrics.
   Google Scholar
• Han, H., and Park, J.Y. (2012), “ARCH/GARCH With Persistent Covariates: Asymptotic Theory of MLE,” Journal of Econometrics, 167, 95–112.
   Web of Science ®Google Scholar
• Han, H., and Park, J.Y. (2013GARCH With Omitted Persistent Covariate, unpublished manuscript, Kyung Hee University.
   Google Scholar
• Hansen, P.R., Huang, Z., and Shek, H.H. (2012), “Realized GARCH: A Complete Model of Returns and Realized Measures of Volatility,” Journal of Applied Econometrics, 27, 877–906.
   Web of Science ®Google Scholar
• Hodrick, R. (1989), “Risk, Uncertainty, and Exchange Rates,” Journal of Monetary Economics, 23, 433–459.
   Web of Science ®Google Scholar
• Hwang, S., and Satchell, S.E. (2005), “GARCH Model With Cross-Sectional Volatility: GARCH-X Models,” Applied Financial Economics, 15, 203–216.
   Google Scholar
• Heber, G., Lunde, A., Shephard, N., and Sheppard, K. (2009), OMI’s Realized Library, Version 0.1, Oxford-Man Institute, University of Oxford.
   Google Scholar
• Jensen, S.T., and Rahbek, A. (2004), “Asymptotic Inference for Nonstationary GARCH,” Econometric Theory, 20, 1203–1226.
   Web of Science ®Google Scholar
• Kasparis, I., Andreou, E., and Phillips, P. C.B. (2012), “Nonparametric Predictive Regression,” unpublished manuscript, University of Cyprus.
   Google Scholar
• Kristensen, D., and Rahbek, A. (2005), “Asymptotics of the QMLE for a Class of ARCH(q) Models,” Econometric Theory, 21, 946–961.
   Web of Science ®Google Scholar
• Kristensen, D., and Rahbek, A. (2010), “Likelihood-Based Inference for Cointegration With Nonlinear Error-Correction,” Journal of Econometrics, 158, 78–94.
   Web of Science ®Google Scholar
• Kristensen, D., and Shin, Y. (2012), “Estimation of Dynamic Models With Nonparametric Simulated Maximum Likelihood,” Journal of Econometrics, 167, 76–94.
   Web of Science ®Google Scholar
• Lamoureux, C.G., and Lastrapes, W.D. (1990), “Heteroskedasticity in Stock Return Data: Volume Versus GARCH Effects,” Journal of Finance, 45, 221–229.
   Web of Science ®Google Scholar
• Marsh, T.A., and Wagner, N. (2005), “Surprise Volume and Heteroskedasticity in Equity Market Returns,” Quantitative Finance, 5, 153–168.
   Web of Science ®Google Scholar
• Park, J.Y., and Phillips, P. C.B. (1999), “Asymptotics for Nonlinear Transformations of Integrated Time Series,” Econometric Theory, 15, 269–298.
   Web of Science ®Google Scholar
• Shephard, N., and Sheppard, K. (2010), “Realising the Future: Forecasting With High Frequency Based Volatility (HEAVY) Models,” Journal of Applied Econometrics, 25, 197–231.
   Web of Science ®Google Scholar
• Wang, Q. (2013), “Martingale Limit Theorem Revisited and Nonlinear Cointegrating Regression” forthcoming in, Econometric Theory.
   Google Scholar
• Wang, Q., and Phillips, P. C.B. (2009a), “Asymptotic Theory for Local Time Density Estimation and Nonparametric Cointegrating Regression,” Econometric Theory, 25, 710–738.
   Web of Science ®Google Scholar
• Wang, Q., and Phillips, P. C.B. (2009b), “Structural Nonparametric Cointegrating Regression,” Econometrica, 77, 1901–1948.
   Web of Science ®Google Scholar
• Yoshihara, K. (1976), “Limiting Behaviour of U-Statistics for Stationary, Absolutely Regular Processes,” Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete, 35, 237–252.
   Web of Science ®Google Scholar