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STOCHASTIC UNIT ROOT MODELS

Published online by Cambridge University Press:  03 November 2006

Christian Gourieroux  and
Christian Y. Robert
Christian Gourieroux
Affiliation:
University of Toronto CREST and CEPREMAP
Christian Y. Robert
Affiliation:
CNAM and CREST
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Abstract

This paper develops a dynamic switching model, with a random walk anda stationary regime, where the time spent in the random walk regimeis endogeneously predetermined. More precisely, we assume that theprocess is recursively defined byYt = μ +Yt−1 +εt, with stochastic probabilityπrw(Yt−1),Yt = μ +εt, with stochastic probability1 −πrw(Yt−1),where (εt) is a strong white noise andπrw is a nondecreasing function.Then, the dynamics of the process(Yt), itsmarginal distribution, and the distribution of the time spent in theunit root regime depend on the pattern of random walk intensityπrw and on the noisedistribution F. Moreover, we study the linksbetween the endogeneous switching regime and the degree ofpersistence of the process(Yt).

Information

Type
Research Article
Information
Econometric Theory , Volume 22 , Issue 6 , December 2006 , pp. 1052 - 1090
Copyright
© 2006 Cambridge University Press

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References

REFERENCES

Asmussen, S. (1987) Applied Probability and Queues. Wiley.Google Scholar
Balke, N.S. & T.B. Fomby (1997) Threshold cointegration. International Economic Review 38, 627–646.CrossRefGoogle Scholar
Bec, F., M. Ben Salem, & M. Carrasco (2004) Test for unit root versus threshold specification with an application to PPP. Journal of Business & Economic Statistics 22, 382–395.CrossRefGoogle Scholar
Billingsley, P. (1995) Probability and Measure, 3rd ed. Wiley Series in Probability and Mathematical Statistics. Wiley.Google Scholar
Bradley, R.C. (2005) Basic properties of strong mixing conditions. A survey and some open questions. Probability Surveys 2, 107–144.CrossRefGoogle Scholar
Brooks, C. & A. Reveiz (2002) A model for exchange rates with crawling bands—An application to the Colombian peso. Journal of Business and Economics 54, 483–503.CrossRefGoogle Scholar
Clark, P.K. (1973) A subordinated stochastic process model with finite variance for speculative prices. Econometrica 41, 135–156.CrossRefGoogle Scholar
Davydov, Y. (1969) On a strong mixing property for Markov chains with a countable number of states. Soviet Doklady 187, 825–827.Google Scholar
Doukhan, P. (1994) Mixing: Properties and Examples. Lecture Notes in Statistics 85, Springer.CrossRefGoogle Scholar
Embrechts, P., C. Klüppelberg, & T. Mikosch (1997) Modelling Extremal Events. Applications of Mathematics. Springer.CrossRefGoogle Scholar
Enders, W. & C. Granger (1998) Unit-root tests and asymmetric adjustment with an example using the term structure of interest rates. Journal of Business & Economic Statistics 16, 304–311.Google Scholar
Engle, R.F. (1982) Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econometrica 50, 987–1008.CrossRefGoogle Scholar
Farnsworth, H. & R. Bass (2003) The term structure with credible and semi-credible targeting. Journal of Finance 58, 839–866.CrossRefGoogle Scholar
Feller, W. (1966) An Introduction to Probability Theory and Its Applications II. Wiley.Google Scholar
Gouriéroux, C. & J. Jasiak (2001) Memory and infrequent break. Economics Letters 70, 29–41.CrossRefGoogle Scholar
Granger, C. & R. Joyeux (1980) An introduction to long-memory time series models and fractional differencing. Journal of Time Series Analysis 1, 15–39.CrossRefGoogle Scholar
Granger, C. & N. Swanson (1997) An introduction to stochastic unit root processes. Journal of Econometrics 80, 35–62.CrossRefGoogle Scholar
Granger, C. & J. Terasvirta (1999) Simple nonlinear time series model with misleading linear properties. Economic Letters 62, 161–165.CrossRefGoogle Scholar
Hamilton, J. (1989) A new approach to the economic analysis of nonstationary time series and the business cycle. Econometrica 5, 357–384.CrossRefGoogle Scholar
Heath, D., S. Resnick, & G. Samorodnitsky (1998) Heavy tails and long range dependence in on/off processes and associated fluid models. Mathematics of Operations Research 23, 145–165.CrossRefGoogle Scholar
MacDonald, I.L. & W. Zucchini (1997) Hidden Markov and Other Models for Discrete-Valued Time Series. Chapman and Hall.Google Scholar
Mandelbrot, B. & H. Taylor (1967) On the distribution of stock prices differences. Operational Research 15, 1057–1062.CrossRefGoogle Scholar
Meyn, S.P. & R.L. Tweedie (1993) Markov Chains and Stochastic Stability. Springer.CrossRefGoogle Scholar
Rahbek, A. & N. Shephard (2002) Inference and Ergodicity in the Autoregressive Conditional Root Model. Discussion paper, University of Oxford.Google Scholar
Sercu, P., R. Uppal, & C. Van Hulle (1995) The exchange rate in the presence of transaction costs: Implications for tests of purchasing power parity. Journal of Finance 50, 1309–1319.CrossRefGoogle Scholar
Shimotsu, K. (2005) Simple (but effective) Tests of Long Memory versus Structural Breaks. Discussion paper, Queen's University.Google Scholar
Tong, H. (1990) Non-linear Time Series—A Dynamical System Approach. Oxford University Press.Google Scholar