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Stationary Processes That Look Like Random Walks The Bounded Random Walk Process In Discrete And Continuous Time

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  • Nicolau, Jo o
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    Abstract

    Several economic and financial time series are bounded by an upper and lower finite limit (e.g., interest rates). It is not possible to say that these time series are random walks because random walks are limitless with probability one (as time goes to infinity). Yet, some of these time series behave just like random walks. In this paper we propose a new approach that takes into account these ideas. We propose a discrete-time and a continuous-time process (diffusion process) that generate bounded random walks. These paths are almost indistinguishable from random walks, although they are stochastically bounded by an upper and lower finite limit. We derive for both cases the ergodic conditions, and for the diffusion process we present a closed expression for the stationary distribution. This approach suggests that many time series with random walk behavior can in fact be stationarity processes.

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    Bibliographic Info

    Article provided by Cambridge University Press in its journal Econometric Theory.

    Volume (Year): 18 (2002)
    Issue (Month): 01 (February)
    Pages: 99-118

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    Handle: RePEc:cup:etheor:v:18:y:2002:i:01:p:99-118_18

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    Cited by:
    1. Rodolfo Cermeño & Bernardo D. Roth & F. Alejandro Villagómez, 2008. "Fiscal Policy and National Saving in Mexico, 1980-2006," Estudios Económicos, El Colegio de México, Centro de Estudios Económicos, vol. 23(2), pages 281-312.
    2. Paulo M. M. Rodrigues & Antonio Rubia, 2004. "On the Small Sample Properties of Dickey Fuller and Maximum Likelihood Unit Root Tests on Discrete-Sampled Short-Term Interest Rates," Econometrics 0405004, EconWPA.
    3. Alex Ferrer & José Casals & Sonia Sotoca, 2014. "A new approach to the unconditional measurement of default risk," Documentos de Trabajo del ICAE 2014-11, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.
    4. Meredith Beechey & Erik Hjalmarsson & Par Osterholm, 2008. "Testing the expectations hypothesis when interest rates are near integrated," International Finance Discussion Papers 953, Board of Governors of the Federal Reserve System (U.S.).
    5. Giuseppe Cavaliere, 2005. "Testing mean reversion in target-zone exchange rates," Applied Economics, Taylor & Francis Journals, vol. 37(20), pages 2335-2347.
    6. Ott, Herve, 2012. "Which factors drive which volatility in the grain sector?," 123rd Seminar, February 23-24, 2012, Dublin, Ireland 122486, European Association of Agricultural Economists.
    7. Magnus Gustavsson & P�R �Sterholm, 2007. "Does Unemployment Hysteresis Equal Employment Hysteresis?," The Economic Record, The Economic Society of Australia, vol. 83(261), pages 159-173, 06.
    8. Gustavsson, Magnus & Österholm, Pär, 2012. "Labor-force participation rates and the informational value of unemployment rates: Evidence from disaggregated US data," Economics Letters, Elsevier, vol. 116(3), pages 408-410.
    9. Clive G. Bowsher & Roland Meeks, 2008. "Stationarity and the term structure of interest rates: a characterisation of stationary and unit root yield curves," Working Papers 0811, Federal Reserve Bank of Dallas.
    10. De-Chih Liu, 2014. "Labor-Force Participation Rates and the Informational Value of Unemployment Rates in US: Evidence from Regional Data," Social Indicators Research, Springer, vol. 116(2), pages 447-455, April.
    11. Niels Haldrup & Robinson Kruse & Timo Teräsvirta & Rasmus T. Varneskov, 2012. "Unit roots, nonlinearities and structural breaks," CREATES Research Papers 2012-14, School of Economics and Management, University of Aarhus.
    12. Cavaliere, Giuseppe & Xu, Fang, 2014. "Testing for unit roots in bounded time series," Journal of Econometrics, Elsevier, vol. 178(P2), pages 259-272.
    13. Hans Genberg & Cho-hoi Hui, 2009. "The Credibility of the Link from the Perspective of Modern Financial Theory," Working Papers 0902, Hong Kong Monetary Authority.

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