Modern Stochastics: Theory and Applications logo


  • Help
Login Register

  1. Home
  2. Issues
  3. Volume 6, Issue 2 (2019)
  4. A copula-based bivariate integer-valued ...

Modern Stochastics: Theory and Applications

Submit your article Information Become a Peer-reviewer
  • Article info
  • Full article
  • Cited by
  • More
    Article info Full article Cited by

A copula-based bivariate integer-valued autoregressive process with application
Volume 6, Issue 2 (2019), pp. 227–249
Andrius Buteikis   Remigijus Leipus  

Authors

 
Placeholder
https://doi.org/10.15559/19-VMSTA130
Pub. online: 12 March 2019      Type: Research Article      Open accessOpen Access

Received
21 August 2018
Revised
12 December 2018
Accepted
28 January 2019
Published
12 March 2019

Abstract

A bivariate integer-valued autoregressive process of order 1 (BINAR(1)) with copula-joint innovations is studied. Different parameter estimation methods are analyzed and compared via Monte Carlo simulations with emphasis on estimation of the copula dependence parameter. An empirical application on defaulted and non-defaulted loan data is carried out using different combinations of copula functions and marginal distribution functions covering the cases where both marginal distributions are from the same family, as well as the case where they are from different distribution families.

References

[1] 
Al-Osh, M., Alzaid, A.: First-order integer-valued autoregressive (INAR(1)) process. J. Time Ser. Anal. 8, 261–275 (1987) MR0903755. https://doi.org/10.1111/j.1467-9892.1987.tb00438.x
[2] 
Barczy, M., Ispány, M., Pap, G., Scotto, M., Silva, M.E.: Innovational outliers in INAR(1) models. Commun. Stat., Theory Methods 39(18), 3343–3362 (2010) MR2747588. https://doi.org/10.1080/03610920903259831
[3] 
Brigo, D., Pallavicini, A., Torresetti, R.: Credit Models and the Crisis: A Journey Into CDOs, Copulas, Correlations and Dynamic Models. Wiley, United Kingdom (2010)
[4] 
Cherubini, U., Mulinacci, S., Gobbi, F., Romagnoli, S.: Dynamic Copula Methods in Finance. Wiley, United Kingdom (2011)
[5] 
Crook, J., Moreira, F.: Checking for asymmetric default dependence in a credit card portfolio: A copula approach. J. Empir. Finance 18, 728–742 (2011)
[6] 
Fenech, J.P., Vosgha, H., Shafik, S.: Loan default correlation using an Archimedean copula approach: A case for recalibration. Econ. Model. 47, 340–354 (2015)
[7] 
Freeland, R.K., McCabe, B.: Asymptotic properties of CLS estimators in the Poisson AR(1) model. Stat. Probab. Lett. 73(2), 147–153 (2005) MR2159250. https://doi.org/10.1016/j.spl.2005.03.006
[8] 
Genest, C., Nešlehová, J.: A primer on copulas for count data. ASTIN Bull. 37(2), 475–515 (2007) MR2422797. https://doi.org/10.2143/AST.37.2.2024077
[9] 
Joe, H.: Dependence Modeling with Copulas. Chapman & Hall/CRC Monographs on Statistics and Applied probability 134 (2015) MR3328438
[10] 
Karlis, D., Pedeli, X.: Flexible bivariate INAR(1) processes using copulas. Commun. Stat., Theory Methods 42, 723–740 (2013) MR3211946. https://doi.org/10.1080/03610926.2012.754466
[11] 
Kedem, B., Fokianos, K.: Regression Models for Time Series Analysis. Wiley-Interscience, New Jersey (2002) MR1933755. https://doi.org/10.1002/0471266981
[12] 
Latour, A.: The multivariate GINAR(p) process. Adv. Appl. Probab. 29(1), 228–248 (1997) MR1432938. https://doi.org/10.2307/1427868
[13] 
Latour, A.: Existence and stochastic structure of a non-negative integer-valued autoregressive process. J. Time Ser. Anal. 19(4), 439–455 (1998) MR1652193. https://doi.org/10.1111/1467-9892.00102
[14] 
Manstavičius, M., Leipus, R.: Bounds for the Clayton copula. Nonlinear Anal., Model. Control 22, 248–260 (2017) MR3608075. https://doi.org/10.15388/na.2017.2.7
[15] 
Nelsen, R.: An Introduction to Copulas, 2nd Edition. Springer (2006) MR2197664. https://doi.org/10.1007/s11229-005-3715-x
[16] 
Pawitan, Y.: In All Likelihood: Statistical Modelling and Inference Using Likelihood. Oxford University Press, New York (2001) MR3668697. https://doi.org/10.1080/00031305.2016.1202140
[17] 
Pedeli, X.: Modelling multivariate time series for count data. PhD thesis, Athens University of Economics and Business (2011)
[18] 
Pedeli, X., Karlis, D.: A bivariate INAR(1) process with application. Stat. Model., Int. J. 11(4), 325–349 (2011) MR2906704. https://doi.org/10.1177/1471082X1001100403
[19] 
Silva, I.M.M.: Contributions to the analysis of discrete-valued time series. PhD thesis, University of Porto (2005)
[20] 
Sklar, M.: Fonctions de répartition à n dimensions et leurs marges. Publ. Inst. Stat. Univ. Paris 8, 229–231 (1959) MR0125600
[21] 
Trivedi, P.K., Zimmer, D.M.: Copula modelling: An introduction for practitioners. Found. Trends Econom. 1(1), 1–111 (2007)

Full article Cited by PDF XML
Full article Cited by PDF XML

Copyright
© 2019 The Author(s). Published by VTeX
by logo by logo
Open access article under the CC BY license.

Keywords
Count data BINAR Poisson negative binomial distribution copula FGM copula Frank copula Clayton copula

MSC2010
60G10 62M10 62H12

Metrics (since March 2018)
870

Article info
views

510

Full article
views

374

PDF
downloads

83

XML
downloads

Export citation

Copy and paste formatted citation
Placeholder

Download citation in file


Share


RSS

MSTA

MSTA

  • Online ISSN: 2351-6054
  • Print ISSN: 2351-6046
  • Copyright © 2018 VTeX

About

  • About journal
  • Indexed in
  • Editors-in-Chief

For contributors

  • Submit
  • OA Policy
  • Become a Peer-reviewer

Contact us

  • ejournals-vmsta@vtex.lt
  • Mokslininkų 2A
  • LT-08412 Vilnius
  • Lithuania
Powered by PubliMill  •  Privacy policy