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Selected Problems in the Analysis of Nonstationary & Nonlinear Time Series

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  • 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
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    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. 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.
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