IDEAS home Printed from https://ideas.repec.org/a/jqe/jqenew/v9y2011i1p1-17.html
   My bibliography  Save this article

Selected Problems in the Analysis of Nonstationary & Nonlinear Time Series

Author

Listed:
  • Dilip M. Nachane

Abstract

There are several reasons why non-linearity and non-stationarity could occur simultaneously in economic models including (i) frictions in markets (ii) asymmetric adjustment mechanisms and (iii) markets (esp. financial markets) being subject to episodes of turbulence and volatility. The task of unravelling nonlinearity from nonstationarity is extremely complex and essentially involves the testing of a sequence of nested hypotheses. In recent years a number of contributions have been occurring in the literature both in the time domain and frequency domain. Several of these approaches are discussed here and we also touch upon the issue of nonlinear cointegration. Both parametric and non-parametric tests for nonlinear cointegration are discussed and their properties analyzed.

Suggested Citation

  • Dilip M. Nachane, 2011. "Selected Problems in the Analysis of Nonstationary & Nonlinear Time Series," Journal of Quantitative Economics, The Indian Econometric Society, vol. 9(1), pages 1-17.
  • Handle: RePEc:jqe:jqenew:v:9:y:2011:i:1:p:1-17
    as

    Download full text from publisher

    File URL: http://www.jqe.co.in/journals/JQE_v9_n1_2011_p1.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Aparicio F. M. & Escribano A., 1998. "Information-Theoretic Analysis of Serial Dependence and Cointegration," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 3(3), pages 1-24, October.
    2. Choi, In & Ahn, Byung Chul, 1995. "Testing for Cointegration in a System of Equations," Econometric Theory, Cambridge University Press, vol. 11(5), pages 952-983, October.
    3. C. W. J. Granger & Jeff Hallman, 1991. "Nonlinear Transformations Of Integrated Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 12(3), pages 207-224, May.
    4. Kwiatkowski, Denis & Phillips, Peter C. B. & Schmidt, Peter & Shin, Yongcheol, 1992. "Testing the null hypothesis of stationarity against the alternative of a unit root : How sure are we that economic time series have a unit root?," Journal of Econometrics, Elsevier, vol. 54(1-3), pages 159-178.
    5. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
    6. Peter Howitt, 1988. "Business Cycles With Costly Search and Recruiting," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 103(1), pages 147-165.
    7. van Dijk, Dick & Franses, Philip Hans & Lucas, Andre, 1999. "Testing for ARCH in the Presence of Additive Outliers," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 14(5), pages 539-562, Sept.-Oct.
    8. Escribano, Álvaro & Mira, Santiago, 1996. "Nonlinear cointegration and nonlinear error correction," DES - Working Papers. Statistics and Econometrics. WS 4546, Universidad Carlos III de Madrid. Departamento de Estadística.
    9. Shin, Yongcheol, 1994. "A Residual-Based Test of the Null of Cointegration Against the Alternative of No Cointegration," Econometric Theory, Cambridge University Press, vol. 10(1), pages 91-115, March.
    10. Floden, Martin, 2000. "Endogenous monetary policy and the business cycle," European Economic Review, Elsevier, vol. 44(8), pages 1409-1429, August.
    11. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    12. Philip Hans Franses & Michael McAleer, 1998. "Testing for Unit Roots and Non‐linear Transformations," Journal of Time Series Analysis, Wiley Blackwell, vol. 19(2), pages 147-164, March.
    13. Hannan, E. J., 1982. "A note on bilinear time series models," Stochastic Processes and their Applications, Elsevier, vol. 12(2), pages 221-224, March.
    14. D. M. Nachane, 1997. "Purchasing power parity: an analysis based on the evolutionary spectrum," Applied Economics, Taylor & Francis Journals, vol. 29(11), pages 1515-1524.
    15. Randal Verbrugge Randal Verbrugge, 1997. "Investigating Cyclical Asymmetries," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 2(1), pages 1-10, April.
    16. T. Subba Rao & M. M. Gabr, 1980. "A Test For Linearity Of Stationary Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 1(2), pages 145-158, March.
    17. Felipe Aparicio & Alvaro Escribano & Ana E. Sipols, 2006. "Range Unit‐Root (RUR) Tests: Robust against Nonlinearities, Error Distributions, Structural Breaks and Outliers," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(4), pages 545-576, July.
    18. Granger, Clive W. J. & Inoue, Tomoo & Morin, Norman, 1997. "Nonlinear stochastic trends," Journal of Econometrics, Elsevier, vol. 81(1), pages 65-92, November.
    19. Artis, Michael J & Bladen-Hovell, Robin & Nachane, Dilip M, 1992. "Instability of the Velocity of Money: A New Approach Based on the Evolutionary Spectrum," CEPR Discussion Papers 735, C.E.P.R. Discussion Papers.
    20. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Kirstin Hubrich & Helmut Lutkepohl & Pentti Saikkonen, 2001. "A Review Of Systems Cointegration Tests," Econometric Reviews, Taylor & Francis Journals, vol. 20(3), pages 247-318.
    2. Matteo Mogliani, 2010. "Residual-based tests for cointegration and multiple deterministic structural breaks: A Monte Carlo study," Working Papers halshs-00564897, HAL.
    3. Zeynel Abidin Ozdemir, 2010. "Dynamics Of Inflation, Output Growth And Their Uncertainty In The Uk: An Empirical Analysis," Manchester School, University of Manchester, vol. 78(6), pages 511-537, December.
    4. Niels Haldrup & Robinson Kruse & Timo Teräsvirta & Rasmus T. Varneskov, 2013. "Unit roots, non-linearities and structural breaks," Chapters, in: Nigar Hashimzade & Michael A. Thornton (ed.), Handbook of Research Methods and Applications in Empirical Macroeconomics, chapter 4, pages 61-94, Edward Elgar Publishing.
    5. Corradi, Valentina & Swanson, Norman R., 2006. "The effect of data transformation on common cycle, cointegration, and unit root tests: Monte Carlo results and a simple test," Journal of Econometrics, Elsevier, vol. 132(1), pages 195-229, May.
    6. Corradi, Valentina & Swanson, Norman R. & White, Halbert, 2000. "Testing for stationarity-ergodicity and for comovements between nonlinear discrete time Markov processes," Journal of Econometrics, Elsevier, vol. 96(1), pages 39-73, May.
    7. Committee, Nobel Prize, 2003. "Time-series Econometrics: Cointegration and Autoregressive Conditional Heteroskedasticity," Nobel Prize in Economics documents 2003-1, Nobel Prize Committee.
    8. Javier Fernandez-Macho, 2013. "A Test for the Null of Multiple Cointegrating Vectors," Economics Series Working Papers 657, University of Oxford, Department of Economics.
    9. Mustapha Baghli, 2004. "Modelling the FF/MM rate by threshold cointegration analysis," Applied Economics, Taylor & Francis Journals, vol. 36(6), pages 533-548.
    10. Mehmet Balcilar & Zeynel Abidin Ozdemir, 2020. "A re-examination of growth and growth uncertainty relationship in a stochastic volatility in the mean model with time-varying parameters," Empirica, Springer;Austrian Institute for Economic Research;Austrian Economic Association, vol. 47(3), pages 611-641, August.
    11. Jansson, Michael, 2004. "Stationarity Testing With Covariates," Econometric Theory, Cambridge University Press, vol. 20(1), pages 56-94, February.
    12. Alan Bartley, William & Lee, Junsoo & Strazicich, Mark C., 2001. "Testing the null of cointegration in the presence of a structural break," Economics Letters, Elsevier, vol. 73(3), pages 315-323, December.
    13. Horváth, Lajos & Liu, Zhenya & Rice, Gregory & Wang, Shixuan, 2020. "Sequential monitoring for changes from stationarity to mild non-stationarity," Journal of Econometrics, Elsevier, vol. 215(1), pages 209-238.
    14. Ignacio Olmeda & Joaquin Pérez, 1995. "Non-linear dynamics and chaos in the Spanish stock market," Investigaciones Economicas, Fundación SEPI, vol. 19(2), pages 217-248, May.
    15. Vasco Gabriel, 2003. "Tests for the Null Hypothesis of Cointegration: A Monte Carlo Comparison," Econometric Reviews, Taylor & Francis Journals, vol. 22(4), pages 411-435.
    16. Doornik, Jurgen A. & Ooms, Marius, 2008. "Multimodality in GARCH regression models," International Journal of Forecasting, Elsevier, vol. 24(3), pages 432-448.
    17. Eleni Constantinou & Robert Georgiades & Avo Kazandjian & George Kouretas, 2005. "Mean and variance causality between the Cyprus Stock Exchange and major equity markets," Working Papers 0501, University of Crete, Department of Economics.
    18. Gadea, Maria Dolores & Sabate, Marcela & Serrano, Jose Maria, 2004. "Structural breaks and their trace in the memory: Inflation rate series in the long-run," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 14(2), pages 117-134, April.
    19. Carnero, María Ángeles & Peña, Daniel & Ruiz Ortega, Esther, 2004. "Spurious and hidden volatility," DES - Working Papers. Statistics and Econometrics. WS ws042007, Universidad Carlos III de Madrid. Departamento de Estadística.
    20. Christoph Hanck & Till Massing, 2021. "Testing for Nonlinear Cointegration under Heteroskedasticity," Papers 2102.08809, arXiv.org, revised Nov 2023.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:jqe:jqenew:v:9:y:2011:i:1:p:1-17. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: D. M. Nachane or the person in charge (email available below). General contact details of provider: https://edirc.repec.org/data/tiesoea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.