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Original Articles

Moment method estimation of first-order continuous-time bilinear processes

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Pages 1070-1087 | Received 07 Feb 2017, Accepted 11 Nov 2017, Published online: 17 Jan 2018

References

  • Ait-Sahalia, Y. 2002. Maximum likelihood estimation of discretely sampled diffusion: A closed-form approximation approach. Econometrica 70 (1):223–62.
  • Arnold, L. 1974. Stochastic differential equations, theory and applications. New York: J. Wiley.
  • Bernet, ∅. 2000. Stochastic differential equations: An introduction with applications. New York: Springer-Verlag.
  • Brockwell, P., E. Chadraa, and A. Lindner. 2006. Continuous-time GARCH processes. Annals. Prob. 16 (2):790–826.
  • Brockwell, P. J. 2001. Continuous-time ARMA processes. Handbook of statistics. 19:249–76. North holland, Amsterdam.
  • Brockwell, P. J., and R. A. Davis. 1987. Time series: Theory and methods. New York: Springer.
  • Chan, K. C., G. A. Karolyi, F. A. Longstaff, and A. B. Sanders. 1992. An empirical comparison of alternative models of the short-term interest rate. Journal of Finance XLVII (3):1209–27.
  • Dacuna-Castte, D., and D. Florens-Zmirou. 1986. Estimation of the coefficient of a diffusion from discrete observations. Stochastics 19:263–84.
  • Haug, S., C. Kluppelberg, and M. Z. Lindner. 2007. Method of moment estimation in the COGARCH(1,1) model. The Econometric Journal 10:320–41.
  • Ibragimov, I. A., and Y. V. Linnik. 1971. Independent and stationary sequences of random variables. Groningen: Wolters- Noordho Publishing.
  • Igloti, E., and G. Terdik. 1999. Bilinear stochastic systems with fractional Brownian motion input. The Annals of Applied Probability 9 (1):46–77.
  • Kallsen, J., and J. Muhle-Karbe. 2011. Methode of moment estimation in time-changed Lévy models. Statistics & Decisions 28:169–94.
  • Kluppelberg, C., A. Lindner, and R. Maller. 2004. A continuous time GARCH process driven by a Lévy process: Stationarity and second order behaviour. J. Appl. Probab. 41:601–22.
  • Le Breton, A., and M. Musiela. 1984. A study of one-dimensional bilinear differential model for stochastic processes. Probability and Mathematical Statistics 4 (1):91–107.
  • Lipcer, R. S., and A. N. Sirjajev. 1978. Statistics of random processes. I, II, Newe York-Heidelberg: Springer-Verlag.
  • Mohler, R. R. 1988. Nonlinear time series and signal processing. Lecture notes in control and information sciences N0.106. Berlin: Springer Verlag.
  • Oesook, L. 2012. Exponential ergodicity and β-mixing property for generalized ornstein-uhlenbeck processes. Theoretical Economics Letters 2:21–25.
  • Prakasa, Rao, B. L. S. 2010. Statistical inference for fractional diffusion processes. United Kingdom: Wiley.
  • Rémillar, B. 2013. Statistical methods for financial engineering. New York: CRC Press. Taylor & Francis Group.
  • Subba, Rao, T., and G. Terdik. 2003. On the theory of discrete and continuous bilinear time series models. Handbook of Statistics 21:827–70.
  • Tsai, H., and K. S. Chan. 2005. Quasi-maximum likelihood estimation for a class of continuous-time long memory processes. J. Time Ser. Analys 26:691–713.
  • van der Vaart, A. W. 1998. Symptotic statistics. Cambridge: Combridge University Press.

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