Abstract
We study the strong consistency of an autoregression parameter of a discrete time Heath-Jarrow-Morton type forward interest rate model, where the interest rate curves are driven by a geometric spatial autoregression field. In this paper the size of the subsamples corresponding to different time points is fixed: the observations of the forward rates are given for the same time to maturity values at each time point. We show the consistency in the stable case and in an unstable case and give empirical results based on simulations as well.
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References
E. Fülöp and G. Pap, Asymptotically optimal tests for a discrete time random field HJM type interest rate model, Acta Sci. Math. (Szeged), 73 (2007), 637–661.
E. Fülöp and G. Pap, Note on strong consistency of maximum likelihood estimators for dependent observations, Proceedings of the 7th International Conference on Applied Informatics (Eger, 2007), vol. I, Eger, B. V. B. Nyomda és Kiadó Kft, 2008, pp. 223–228.
E. Fülöp and G. Pap, Strong consistency of maximum likelihood estimators for a discrete time random field HJM type interest rate model, Lithuanian Math. J., 49 (2009), 5–25.
J. Gáll, Some Problems in Discrete Time Financial Market Models, Ph.D. Dissertation, Debrecen, 2008.
J. Gáll, G. Pap and W. Peeters, Random field forward interest rate models, market price of risk and their statistics, Ann. Univ. Ferrara Sez. VII Sci. Mat., 53 (2007), 233–242.
J. Gáll, G. Pap and M. von Zuijlen, Maximum likelihood estimator of the volatility of forward rates driven by geometric spatial AR sheet, J. Appl.Math., 2004 (2004), 293–309.
J. Gáll, G. Pap and M. von Zuijlen, Joint ML estimation of all parameters in a discrete time random field HJM type interest rate model, Radboud University Nijmegen, Report No. 0606, 2006.
J. Gáll, G. Pap and M. von Zuijlen, Forward interest rate curves in discrete time settings driven by random fields, Comput.Math.Appl., 51 (2006), 387–396.
R. D. H. Heijmans and J. R. Magnus, Consistent maximum-likelihood estimation with dependent observations: The general (non-normal) case and the normal case, J. Econometrics, 32 (1986), 253–285.
R. I. Jennrich, Asymptotic properties of non-linear least squares estimators, Ann. Math. Statist., 40 (1969), 633–643.
L. Le Cam, Asymptotic Methods in Statistical Decision Theory, Springer-Verlag, New York, 1986.
W. Peeters, Volatility estimation for different structures of random field interest rate models in discrete time, Publ. Math. Debrecen, 72 (2008), 317–334.
R Development Core Team, R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing, Vienna, Austria, 2008.
A.W. van der Vaart, Asymptotic Statistics, Cambridge University Press, Cambridge, 1998.
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Communicated by G. Pap
This research was supported by the European Union and Hungary, co-financed by the European Social Fund in the framework of TÁMOP 4.2.4.A/2-11-1-2012-0001 ‘National Excellence Program’.
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Fülöp, E. Strong consistency of parameter estimators and simulations in a forward interest rate model. ActaSci.Math. 80, 327–348 (2014). https://doi.org/10.14232/actasm-014-020-z
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DOI: https://doi.org/10.14232/actasm-014-020-z
Key words and phrases
- HJM forward interest rate models
- geometric spatial autoregression field
- strong consistency of ML estimators
- simulations with R