Hostname: page-component-7bb8b95d7b-qxsvm Total loading time: 0 Render date: 2024-09-12T10:27:40.684Z Has data issue: false hasContentIssue false
  • English
  • Français

REGIME-SWITCHING AUTOREGRESSIVE COEFFICIENTS AND THE ASYMPTOTICS FOR UNIT ROOT TESTS

Published online by Cambridge University Press:  22 April 2008

Giuseppe Cavaliere  and
Iliyan Georgiev
Giuseppe Cavaliere
Affiliation:
Università di Bologna
Iliyan Georgiev*
Affiliation:
Universidade Nova de Lisboa
*
Address correspondence to Iliyan Georgiev, Faculdade de Economia, Universidade Nova de Lisboa, Campus de Campolide, PT 1099-032, Lisboa, Portugal; e-mail: [email protected].
Get access Rights & Permissions [Opens in a new window]

Abstract

Most of the asymptotic results for Markov regime-switching models with possible unit roots are based on specifications implying that the number of regime switches grows to infinity as the sample size increases. Conversely, in this note we derive some new asymptotic results for the case of Markov regime switches that are infrequent in the sense that their number is bounded in probability, even asymptotically. This is achieved by (inversely) relating the probability of regime switching to the sample size. The proposed asymptotic theory is applied to a well-known stochastic unit root model, where the dynamics of the observed variable switches between a unit root regime and a stationary regime.

Type
Notes and Problems
Information
Econometric Theory , Volume 24 , Issue 4 , August 2008 , pp. 1137 - 1148
Copyright
Copyright © Cambridge University Press 2008

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.)

References

REFERENCES

Ang, A. ’ Bekaert, G. (2002) Regime switches in interest rates. Journal of Business ’ Economics Statistics 20, 163–182.CrossRefGoogle Scholar
Balke, N.S. ’ Fomby, T.B. (1991a) Shifting trends, segmented trends, and infrequent permanent shocks. Journal of Monetary Economics 28, 61–85.CrossRefGoogle Scholar
Balke, N.S. ’ Fomby, T.B. (1991b) Infrequent permanent shocks and the finite-sample performance of unit root tests. Economics Letters 36, 269–273.Google Scholar
Balke, N.S. ’ Fomby, T.B. (1994) Large shocks, small shocks and economic fluctuations: Outliers in macroeconomic time series. Journal of Applied Econometrics 9, 181–200.CrossRefGoogle Scholar
Billingsley, P. (1968) Convergence of Probability Measures. Wiley.Google Scholar
Cavaliere, G. (2003) Asymptotics for unit root tests under Markov regime-switching. Econometrics Journal 6, 193–216.Google Scholar
Diebold, F.X. ’ Inoue, A. (2001) Long memory and regime switching. Journal of Econometrics 105, 131–159.Google Scholar
Gourieroux, C. ’ Roberts, C.Y. (2006) Stochastic unit root models. Econometric Theory 22, 1052–1090.Google Scholar
Hamilton, J.D. (1989) A new approach to the economic analysis of non-stationary time series and the business cycle. Econometrica 57, 357–384.Google Scholar
Kurtz, T. ’ Protter, P. (1991) Weak limit theorems for stochastic integrals and stochastic differential equations. Annals of Probability 19, 1035–1070.Google Scholar
Lin, Z. (1997) The invariance principle for some class of Markov chains. Theory of Probability and Its Applications 44, 136–140.CrossRefGoogle Scholar
Nelson, C.R., Piger, J., ’ Zivot, E. (2001) Markov regime-switching and unit root tests. Journal of Business ’ Economic Statistics 19, 404–415.CrossRefGoogle Scholar
Perron, P. (1989) The great crash, the oil price shock, and the unit root hypothesis. Econometrica 57, 1361–1401.Google Scholar
Phillips, P.C.B. ’ Solo, V. (1992) Asymptotics for linear processes. Annals of Statistics 20, 971–1001.CrossRefGoogle Scholar
Psaradakis, Z. (2001) Markov level shifts and the unit root hypothesis. Econometrics Journal 4, 226–242.Google Scholar
Råde, L. (1976) The two-state Markov process and additional events. American Mathematical Monthly 83, 354–356.Google Scholar
Rahbek, A. ’ Shephard, N. (2002) Inference and Ergodicity in the Autoregressive Conditional Root Model. Economics Working paper 2002-W7, Nuffield College.Google Scholar