A copula-based bivariate integer-valued autoregressive process with application

Buteikis, Andrius; Leipus, Remigijus

doi:10.15559/19-VMSTA130

Modern Stochastics: Theory and Applications

A copula-based bivariate integer-valued autoregressive process with application

Volume 6, Issue 2 (2019), pp. 227–249

Andrius Buteikis Remigijus Leipus

https://doi.org/10.15559/19-VMSTA130

Pub. online: 12 March 2019 Type: Research Article

Open 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)

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Keywords

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

MSC2010

60G10 62M10 62H12

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