Hostname: page-component-76d6cb85b7-2r2wp Total loading time: 0 Render date: 2026-07-21T11:12:53.196Z Has data issue: false hasContentIssue false
  • English
  • Français

TIME IRREVERSIBLE COPULA-BASED MARKOV MODELS

Published online by Cambridge University Press:  16 April 2014

Brendan K. Beare  and
Juwon Seo
Brendan K. Beare*
Affiliation:
University of California, San Diego
Juwon Seo
Affiliation:
University of California, San Diego
*
*Address correspondence to Brendan Beare, Department of Economics, University of California-San Diego, 9500 Gilman Drive #0508, La Jolla, CA 92093-0508. E-mail: bbeare@ucsd.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

Economic and financial time series frequently exhibit time irreversible dynamics. For instance, there is considerable evidence of asymmetric fluctuations in many macroeconomic and financial variables, and certain game theoretic models of price determination predict asymmetric cycles in price series. In this paper, we make two primary contributions to the econometric literature on time reversibility. First, we propose a new test of time reversibility, applicable to stationary Markov chains. Compared to existing tests, our test has the advantage of being consistent against arbitrary violations of reversibility. Second, we explain how a circulation density function may be used to characterize the nature of time irreversibility when it is present. We propose a copula-based estimator of the circulation density and verify that it is well behaved asymptotically under suitable regularity conditions. We illustrate the use of our time reversibility test and circulation density estimator by applying them to five years of Canadian gasoline price markup data.

Information

Type
ARTICLES
Information
Econometric Theory , Volume 30 , Issue 5 , October 2014 , pp. 923 - 960
Copyright
Copyright © Cambridge University Press 2014 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

REFERENCES

Abegaz, F. & Naik-Nimbalkar, U.V. (2008) Dynamic copula-based Markov time series. Communications in Statistics – Theory and Methods 37, 2447–2460.CrossRefGoogle Scholar
Andrews, D.W.K. & Pollard, D. (1994) An introduction to functional central limit theorems for dependent stochastic processes. International Statistical Review 62, 119–132.CrossRefGoogle Scholar
Beare, B.K. (2010) Copulas and temporal dependence. Econometrica 78, 395–410.Google Scholar
Beare, B.K. (2012) Archimedean copulas and temporal dependence. Econometric Theory 28, 1165–1185.Google Scholar
Belaire-Franch, J. & Contreras, D. (2004) A power comparison among tests for time reversibility. Economics Bulletin 3, 1–17.Google Scholar
Bouyé, E. & Salmon, M. (2009) Dynamic copula quantile regressions and tail area dynamic dependence in Forex markets. European Journal of Finance 15, 721–750.Google Scholar
Bradley, R.C. (2007) Introduction to Strong Mixing Conditions, vol. 1. Kendrick Press.Google Scholar
Bücher, A. & Ruppert, M. (2013) Consistent testing for a constant copula under strong mixing based on the tapered block multiplier technique. Journal of Multivariate Analysis 116, 208–229.Google Scholar
Cason, T.N., Friedman, D., & Wagener, F. (2005) The dynamics of price dispersion, or Edgeworth variations. Journal of Economic Dynamics and Control 29, 801–822.Google Scholar
Chang, J.T. & Pollard, D. (1997) Conditioning as disintegration. Statistica Neerlandica 51, 287–317.Google Scholar
Chen, Y.-T. (2003) Testing serial independence against time irreversibility. Studies in NonlinearDynamics and Econometrics 7, 1–28.Google Scholar
Chen, Y.-T., Chou, R.Y., & Kuan, C.-M. (2000) Testing time reversibility without moment restrictions. Journal of Econometrics 95, 199–218.Google Scholar
Chen, X. & Fan, Y. (2006) Estimation of copula-based semiparametric time series models. Journal of Econometrics 130, 307–335.CrossRefGoogle Scholar
Chen, X., Koenker, R., & Xiao, Z. (2009) Copula-based nonlinear quantile autoregression. Econometrics Journal 12, S50–S67.Google Scholar
Chen, Y.-T. & Kuan, C.M. (2002) Time irreversibility and EGARCH effects in US stock index returns. Journal of Applied Econometrics 17, 565–578.CrossRefGoogle Scholar
Chen, X., Wu, W.B., & Yi, Y. (2009) Efficient estimation of copula-based semiparametric Markov models. Annals of Statistics 37, 4214–4253.Google Scholar
Cherubini, U., Mulinacci, S., Gobbi, F., & Romagnoli, S. (2011) Dynamic Copula Methods in Finance. Wiley Finance Series. Wiley.CrossRefGoogle Scholar
Darolles, S., Florens, J.-P., & Gouriéroux, C. (2004) Kernel-based nonlinear canonical analysis and time reversibility. Journal of Econometrics 119, 323–353.Google Scholar
Darsow, W.F., Nguyen, B., & Olsen, E.T. (1992) Copulas and Markov processes. Illinois Journal of Mathematics 36, 600–642.Google Scholar
de la Peña, V., Ibragimov, R., & Sharakhmetov, S. (2006) Characterizations of joint distributions, copulas, information, dependence and decoupling, with applications to time series. In Rojo, J. (ed.),2nd Erich L. Lehmann Symposium – Optimality. IMS Lecture Notes - Monograph Series 49,183–209.Google Scholar
DeLong, J.B. & Summers, L.H. (1986) Are business cycles symmetrical? In Gordon, R.J. (ed.), The American Business Cycle: Continuity and Change. University of Chicago Press.Google Scholar
Eckert, A. (2002) Retail price cycles and response asymmetry. Canadian Journal of Economics 35, 52–77.Google Scholar
Eckert, A. (2003) Retail price cycles and presence of small firms. International Journal of Industrial Organization 21, 151–170.Google Scholar
Fermanian, J.-D. & Scaillet, O. (2003) Nonparametric estimation of copulas for time series. Journal of Risk 5, 25–54.Google Scholar
Gagliardini, P. & Gouriéroux, C. (2008) Duration time-series models with proportional hazard. Journal of Time Series Analysis 29, 74–124.Google Scholar
Genest, C., Ghoudi, K., & Rivest, L.-P. (1998) Comment on the article of E. W. Frees and E. A. Valdez entitled “Understanding relationships using copulas”. North American Actuarial Journal 2,143–149.CrossRefGoogle Scholar
Genest, C., Nešlehová, J., & Quessy, J.-F. (2012) Tests for symmetry for bivariate copulas. Annalsof the Institute of Statistical Mathematics 64, 811–834.Google Scholar
Hamilton, J.D. (2009) Causes and consequences of the oil shock of 2007–08. Brookings Papers on Economic Activity Spring, 215–259.Google Scholar
Hinich, M.J. & Rothman, P. (1998) Frequency-domain test of time reversibility. Macroeconomic Dynamics 2, 72–88.Google Scholar
Ibragimov, R. (2009) Copula-based characterizations for higher-order Markov processes. Econometric Theory 25, 819–846.Google Scholar
Ibragimov, I. & Müller, U.K. (2010) t-Statistic based correlation and heterogeneity robust inference. Journal of Business and Economic Statistics 28, 453–468.Google Scholar
Keynes, J.M. (1936) The General Theory of Employment, Interest and Money. Macmillan.Google Scholar
Khoudraji, A. (1995) Contributions à l’étude des copules et à la modélisation de valeurs extrêmes bivariées. Ph.D. thesis, Université Laval, Québec City.Google Scholar
Lancaster, H.O. (1958) The structure of bivariate distributions. Annals of Mathematical Statistics 29, 719–736.Google Scholar
Lewis, M.S. & Noel, M.D. (2011) The speed of gasoline price response in markets with and without Edgeworth cycles. Review of Economics and Statistics 93, 672–682.Google Scholar
Liebscher, E. (2008) Construction of asymmetric multivariate copulas. Journal of Multivariate Analysis 99, 2234–2250.Google Scholar
Maskin, E. & Tirole, J. (1988) A theory of dynamic oligopoly II: Price competition, kinked demand curves and Edgeworth cycles. Econometrica 56, 571–599.CrossRefGoogle Scholar
McCausland, W.J. (2007) Time reversibility of stationary regular finite-state Markov chains. Journal of Econometrics 136, 303–318.Google Scholar
Neftçi, S.N. (1984) Are economic time series asymmetric over the business cycle? Journal of Political Economy 92, 307–328.Google Scholar
Nelsen, R.B. (2006) An Introduction to Copulas, 2nd ed. Springer-Verlag.Google Scholar
Nelsen, R.B. (2007) Extremes of nonexchangeability. Statistical Papers 48, 329–336.Google Scholar
Noel, M.D. (2007) Edgeworth price cycles, cost-based pricing and sticky pricing in retail gasoline markets. Review of Economics and Statistics 89, 324–334.CrossRefGoogle Scholar
Noel, M.D. (2008) Edgeworth cycles and focal prices: Computational dynamic Markov equilibria. Journal of Economics and Management Strategy 17, 345–377.Google Scholar
Noel, M.D. (2011) Edgeworth price cycles. In Durlauf, S.N. & Blume, L.E. (eds.), New Palgrave Dictionary of Economics. Palgrave Macmillan.Google Scholar
Paparoditis, E. & Politis, D.N. (1998) The backward local bootstrap for conditional predictive inference in nonlinear time series. In Lipitakis, E.A. (ed.), Proceedings of the 4th Hellenic European Conference on Computer Mathematics and Its Applications. Lea Publishing.Google Scholar
Paparoditis, E. & Politis, D.N. (2001) A Markovian local resampling scheme for nonparametric estimators in time series analysis. Econometric Theory 17, 540–566.Google Scholar
Paparoditis, E. & Politis, D.N. (2002) The local bootstrap for Markov processes. Journal of Statistical Planning and Inference 108, 301–328.Google Scholar
Peltzman, S. (2000) Prices rise faster than they fall. Journal of Political Economy 108, 466–502.Google Scholar
Pollard, D. (1990) Empirical Processes: Theory and Applications. Institute of Mathematical Statistics.Google Scholar
Psaradakis, Z. (2008) Assessing time reversibility under minimal assumptions. Journal of Time Series Analysis 29, 881–905.Google Scholar
Racine, J.S. & Maasoumi, E. (2007) A versatile and robust metric entropy test of time-reversibility, and other hypotheses. Journal of Econometrics 138, 547–567.Google Scholar
Radulović, D. (2002) On the bootstrap and empirical processes for dependent sequences. In Dehling, H., Mikosch, T., & Sųrensen, M. (eds.), Empirical Process Techniques for Dependent Data. Birkhäuser.Google Scholar
Ramsey, J.B. & Rothman, P. (1996) Time irreversibility and business cycle asymmetry. Journal of Money, Credit and Banking 28, 1–21.Google Scholar
Rémillard, B. & Scaillet, O. (2009) Testing for equality between two copulas. Journal of Multivariate Analysis 100, 377–386.Google Scholar
Rio, E. (2000) Théorie Asymptotique des Processus Aléatoires Faiblement Dépendants. Springer-Verlag.Google Scholar
Robinson, P.M. (1983) Nonparametric estimators for time series. Journal of Time Series Analysis 4, 185–207.Google Scholar
Rothman, P. (1991) Further evidence on the asymmetric behavior of unemployment rates over the business cycle. Journal of Macroeconomics 13, 291–298.Google Scholar
Scaillet, O. (2005) A Kolmogorov-Smirnov type test for positive quadrant dependence. Canadian Journal of Statistics 33, 415–427.Google Scholar
Sharifdoost, M., Mahmoodi, S., & Pasha, E. (2009) A statistical test for time reversibility of stationary finite state Markov chains. Applied Mathematical Sciences 52, 2563–2574.Google Scholar
Tappata, M. (2009) Rockets and feathers: Understanding asymmetric pricing. RAND Journal of Economics 40, 673–687.CrossRefGoogle Scholar
van der Vaart, A.W. & Wellner, J.A. (1996) Weak Convergence and Empirical Processes. Springer-Verlag.Google Scholar
Wang, Z. (2009) (Mixed) strategy in oligopoly pricing: Evidence from gasoline price cycles before and under a timing regulation. Journal of Political Economy 117, 987–1030.CrossRefGoogle Scholar