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Descriptive econometrics for non-stationary time series with empirical illustrations

Author

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  • Peter C. B. Phillips

    (Cowles Foundation for Research in Economics, Yale University, PO Box 208281, New Haven, CT 06520-8281, USA)

Abstract

Recent work by the author on methods of spatial density analysis for time series data with stochastic trends is reviewed. The methods are extended to include processes with deterministic trends, formulae for the mean spatial density are given, and the limits of sample moments of non-stationary data are shown to take the form of moments with respect to the underlying spatial density, analogous to population moments of a stationary process. The methods are illustrated in some empirical applications and simulations. The empirical applications include macroeconomic data on inflation, financial data on exchange rates and political opinion poll data. It is shown how the methods can be used to measure empirical hazard rates for inflation and deflation. Empirical estimates based on historical US data over the last 60 years indicate that the predominant inflation risks are at low levels (2-6%) and low two-digit levels (10-12%), and that there is also a significant risk of deflation around the −1% level. Copyright © 2001 John Wiley & Sons, Ltd.

Suggested Citation

  • Peter C. B. Phillips, 2001. "Descriptive econometrics for non-stationary time series with empirical illustrations," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 16(3), pages 389-413.
  • Handle: RePEc:jae:japmet:v:16:y:2001:i:3:p:389-413
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    File URL: http://qed.econ.queensu.ca:80/jae/2001-v16.3/
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    References listed on IDEAS

    as
    1. Peter C.B. Phillips, 1987. "Multiple Regression with Integrated Time Series," Cowles Foundation Discussion Papers 852, Cowles Foundation for Research in Economics, Yale University.
    2. Hardle, Wolfgang & Linton, Oliver, 1986. "Applied nonparametric methods," Handbook of Econometrics,in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 38, pages 2295-2339 Elsevier.
    3. Sims, Christopher A, 1980. "Macroeconomics and Reality," Econometrica, Econometric Society, vol. 48(1), pages 1-48, January.
    4. Phillips, P.C.B., 1986. "Understanding spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 33(3), pages 311-340, December.
    5. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    6. Espasa, Antoni & Sargan, J Denis, 1977. "The Spectral Estimation of Simultaneous Equation Systems with Lagged Endogenous Variables," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 18(3), pages 583-605, October.
    7. Paul R. Krugman, 1991. "Target Zones and Exchange Rate Dynamics," The Quarterly Journal of Economics, Oxford University Press, vol. 106(3), pages 669-682.
    8. Peter C.B. Phillips & Joon Y. Park, 1998. "Nonstationary Density Estimation and Kernel Autoregression," Cowles Foundation Discussion Papers 1181, Cowles Foundation for Research in Economics, Yale University.
    9. Lars E. O. Svensson, 1992. "An Interpretation of Recent Research on Exchange Rate Target Zones," Journal of Economic Perspectives, American Economic Association, vol. 6(4), pages 119-144, Fall.
    10. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    11. Peter C. B. Phillips, 1998. "New Tools for Understanding Spurious Regressions," Econometrica, Econometric Society, vol. 66(6), pages 1299-1326, November.
    12. Peter C.B. Phillips, 1998. "Econometric Analysis of Fisher's Equation," Cowles Foundation Discussion Papers 1180, Cowles Foundation for Research in Economics, Yale University.
    13. Hardle, Wolfgang & Linton, Oliver, 1986. "Applied nonparametric methods," Handbook of Econometrics,in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 38, pages 2295-2339 Elsevier.
    14. Paul Krugman & Marcus Miller, 1992. "Exchange Rate Targets and Currency Bands," NBER Books, National Bureau of Economic Research, Inc, number krug92-1, January.
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    Cited by:

    1. Xu, Ke-Li, 2010. "Reweighted Functional Estimation Of Diffusion Models," Econometric Theory, Cambridge University Press, vol. 26(02), pages 541-563, April.
    2. Xu, Ke-Li, 2009. "Empirical likelihood-based inference for nonparametric recurrent diffusions," Journal of Econometrics, Elsevier, vol. 153(1), pages 65-82, November.
    3. Hong, Seung Hyun & Phillips, Peter C. B., 2010. "Testing Linearity in Cointegrating Relations With an Application to Purchasing Power Parity," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(1), pages 96-114.
    4. Wang, Qiying & Phillips, Peter C.B., 2009. "Asymptotic Theory For Local Time Density Estimation And Nonparametric Cointegrating Regression," Econometric Theory, Cambridge University Press, vol. 25(03), pages 710-738, June.
    5. Phillips, Peter C.B. & Jin, Sainan & Hu, Ling, 2007. "Nonstationary discrete choice: A corrigendum and addendum," Journal of Econometrics, Elsevier, vol. 141(2), pages 1115-1130, December.
    6. Jiti Gao & Peter C.B. Phillips, 2011. "Semiparametric Estimation in Multivariate Nonstationary Time Series Models," Monash Econometrics and Business Statistics Working Papers 17/11, Monash University, Department of Econometrics and Business Statistics.
    7. Phillips, Peter C. B., 2001. "Trending time series and macroeconomic activity: Some present and future challenges," Journal of Econometrics, Elsevier, vol. 100(1), pages 21-27, January.
    8. Ling Hu & Peter C.B. Phillips, 2002. "Dynamics of the Federal Funds Target Rate: A Nonstationary Discrete Choice Approach," Cowles Foundation Discussion Papers 1365, Cowles Foundation for Research in Economics, Yale University.
    9. Chan, Nigel & Wang, Qiying, 2015. "Nonlinear regressions with nonstationary time series," Journal of Econometrics, Elsevier, vol. 185(1), pages 182-195.
    10. Kasparis, Ioannis & Phillips, Peter C.B., 2012. "Dynamic misspecification in nonparametric cointegrating regression," Journal of Econometrics, Elsevier, vol. 168(2), pages 270-284.
    11. Gao, Jiti & Phillips, Peter C.B., 2013. "Semiparametric estimation in triangular system equations with nonstationarity," Journal of Econometrics, Elsevier, vol. 176(1), pages 59-79.
    12. Phillips, Peter C.B., 2009. "Local Limit Theory And Spurious Nonparametric Regression," Econometric Theory, Cambridge University Press, vol. 25(06), pages 1466-1497, December.

    More about this item

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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