Project Euclid

References

• [1] Andrews, D.W.K. (1999) Estimation when a parameter is on a boundary. Econometrica, 67, 1341- 1384.
• [2] Berkes, I. and Horváth, L. (2003a) The efficiency of the estimators of the parameters in GARCH processes. Ann. Statist. To appear. Abstract can also be found in the ISI/STMA publication
  URL: STMA abstract
  
• [3] Berkes, I. and Horváth, L. (2003b) The rate of consistency of the quasi-maximum likelihood estimator. Statist. Probab. Lett., 61, 133-143. Abstract can also be found in the ISI/STMA publication
  URL: STMA abstract
  
• [4] Berkes, I., Horváth, L. and Kokoszka, P.S. (2003) GARCH processes: structure and estimation. Bernoulli, 9, 201-227. Abstract can also be found in the ISI/STMA publication
  URL: STMA abstract
  
• [5] Billingsley, P. (1961) The Lindeberg-Levy theorem for martingales. Proc. Amer. Math. Soc., 12, 788-792.
• [6] Billingsley, P. (1995) Probability and Measure. New York: Wiley.
• [7] Bollerslev, T. (1986) Generalized autoregressive conditional heteroskedasticity. J. Econometrics, 31, 307-327. Abstract can also be found in the ISI/STMA publication
  URL: STMA abstract
  
• [8] Bougerol, P. and Picard, N. (1992) Stationarity of GARCH processes and of some nonnegative time series. J. Econometrics, 52, 115-127. Abstract can also be found in the ISI/STMA publication
  URL: STMA abstract
  
• [9] Boussama, F. (1998) Ergodicité, mélange et estimation dans les modèles GARCH. Doctoral thesis, Université Paris 7.
• [10] Boussama, F. (2000) Normalité asymptotique de l´estimateur du pseudo-maximum de vraisemblance d´un modèle GARCH. C. R. Acad, Sci. Paris, 331, 81-84.
• [11] Brockwell, P.J. and Davis, R.A. (1991) Time Series: Theory and Methods. New York: Springer-Verlag.
• [12] Chen, M. and An, H.Z. (1998) A note on the stationarity and the existence of moments of the GARCH model. Statist. Sinica, 8, 505-510. Abstract can also be found in the ISI/STMA publication
  URL: STMA abstract
  
• [13] Davis, R.A., Knight, K. and Liu, J. (1992) M-estimation for autoregressions with infinite variance. Stochastic Process. Appl., 40, 145-180.
• [14] Engle, R.F. (1982) Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econometrica, 50, 987-1007.
• [15] Kingman, J.F.C. (1973) Subadditive ergodic theory. Ann. Probab., 6, 883-909.
• [16] Kokoszka, P.S. and Taqqu, M.S. (1996) Parameter estimation for infinite variance fractional ARIMA. Ann. Statist., 24, 1880-1913. Abstract can also be found in the ISI/STMA publication
  URL: STMA abstract
  
• [17] Lee, S.-W. and Hansen, B.E. (1994) Asymptotic theory for the GARCH(1, 1) quasi-maximum likelihood estimator. Econometric Theory, 10, 29-52. Abstract can also be found in the ISI/STMA publication
  URL: STMA abstract
  
• [18] Ling, S. and Li, W.K. (1997) On fractionally integrated autoregressive moving-average time series models with conditional heteroscedasticity. J. Amer. Statist. Assoc., 92, 1184-1194. Abstract can also be found in the ISI/STMA publication
  URL: STMA abstract
  
• [19] Ling, S. and Li, W.K. (1998) Limiting distributions of maximum likelihood estimators for unstable ARMA models with GARCH errors. Ann Statist., 26, 84-125. Abstract can also be found in the ISI/STMA publication
  URL: STMA abstract
  
• [20] Ling, S. and Li, W.K. (2003) Asymptotic inference for unit root processes with GARCH(1, 1) errors. Econometric Theory, 19, 541-564.
• [21] Ling, S. and McAleer, M. (2003a) Asymptotic theory for a vector ARMA-GARCH model. Econometric Theory, 19, 280-310.
• [22] Ling, S. and McAleer, M. (2003b) On adaptative estimation in nonstationary ARMA models with GARCH errors. Ann. Statist., 31, 642-674.
• [23] Lumsdaine, R.L. (1996) Consistency and asymptotic normality of the quasi-maximum likelihood estimator in IGARCH(1, 1) and covariance stationary GARCH(1, 1) models. Econometrica, 64, 575-596. Abstract can also be found in the ISI/STMA publication
  URL: STMA abstract
  
• [24] Mikosch, T. (2001) Modeling financial time series. Notes for lecture on "Modeling heavy tails and dependence in financial data" presented to the meeting on "New Directions in Time Series Analysis", Centre International de Rencontres Mathématiques, Luminy, France.
• [25] Mikosch, T., Gadrich, T., Klüppelberg, C. and Adler, R.J. (1995) Parameter estimation for ARMA models with infinite variance innovations. Ann. Statist., 23, 305-326. Abstract can also be found in the ISI/STMA publication
  URL: STMA abstract
  
• [26] Nelson, D.B. (1990) Stationarity and persistence in the GARCH(1, 1) model. Econometric Theory, 6, 318-334.
• [27] Straumann, D. and Mikosch, T. (2003) Quasi-maximum-likelihood estimation in heteroscedastic time series: a stochastic recurrence equation approach. Technical report, University of Copenhagen.
• [28] Weiss, A.A. (1986) Asymptotic theory for ARCH models: estimation and testing. Econometric Theory, 2, 107-131.