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A spectral analysis of New Zealand output gaps using Fourier and wavelet techniques

This paper uses frequency domain techniques to illustrate the properties of various measures of New Zealand's output gap. Measures of the output gap are estimated using a number of different methods: a Structural VAR model, a multivariate unobserved components model, the Hodrick-Prescott filter, a multivariate time series filter, and a linear time trend filter. Spectral densities, calculated using the Fourier transform, highlight a number of important differences in the cyclical properties of the various output gap measures. However, the Fourier transform requires time series to be (weakly) stationary. This may be an unreasonable assumption for New Zealand data given our recent economic history. Accordingly, the paper also uses time-dependant spectra, calculated using wavelet analysis, to further illustrate the cyclical characteristics of the different techniques used to estimate the output gap.

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File URL: http://www.rbnz.govt.nz/research_and_publications/discussion_papers/2000/dp00_6.pdf
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Paper provided by Reserve Bank of New Zealand in its series Reserve Bank of New Zealand Discussion Paper Series with number DP2000/06.

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Length: 20p
Date of creation: Jun 2000
Date of revision:
Handle: RePEc:nzb:nzbdps:2000/06
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  1. Chantal Dupasquier & Alain Guay & Pierre St-Amant, 1997. "A Comparison of Alternative Methodologies for Estimating Potential Output and the Output Gap," Working Papers 97-5, Bank of Canada.
  2. Timothy Cogley & James M. Nason, 1993. "Effects of the Hodrick-Prescott filter on trend and difference stationary time series: implications for business cycle research," Working Papers in Applied Economic Theory 93-01, Federal Reserve Bank of San Francisco.
  3. Canova, Fabio, 1993. "Detrending and Business Cycle Facts," CEPR Discussion Papers 782, C.E.P.R. Discussion Papers.
  4. Gregory, Allan W & Smith, Gregor W, 1995. "Business Cycle Theory and Econometrics," Economic Journal, Royal Economic Society, vol. 105(433), pages 1597-1608, November.
  5. Robert J. Hodrick & Edward Prescott, 1981. "Post-War U.S. Business Cycles: An Empirical Investigation," Discussion Papers 451, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  6. Marianne Baxter & Robert G. King, 1995. "Measuring Business Cycles Approximate Band-Pass Filters for Economic Time Series," NBER Working Papers 5022, National Bureau of Economic Research, Inc.
  7. Cochrane, John H, 1994. "Permanent and Transitory Components of GNP and Stock Prices," The Quarterly Journal of Economics, MIT Press, vol. 109(1), pages 241-65, February.
  8. Harvey, A C & Jaeger, A, 1993. "Detrending, Stylized Facts and the Business Cycle," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(3), pages 231-47, July-Sept.
  9. King, Robert G. & Plosser, Charles I. & Rebelo, Sergio T., 1988. "Production, growth and business cycles : I. The basic neoclassical model," Journal of Monetary Economics, Elsevier, vol. 21(2-3), pages 195-232.
  10. Ramsey James B. & Lampart Camille, 1998. "The Decomposition of Economic Relationships by Time Scale Using Wavelets: Expenditure and Income," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 3(1), pages 1-22, April.
  11. Nelson, Charles R. & Plosser, Charles I., 1982. "Trends and random walks in macroeconmic time series : Some evidence and implications," Journal of Monetary Economics, Elsevier, vol. 10(2), pages 139-162.
  12. Paul Conway & Ben Hunt, 1997. "Estimating potential output: a semi-structural approach," Reserve Bank of New Zealand Discussion Paper Series G97/9, Reserve Bank of New Zealand.
  13. Jane T. Haltmaier, 1996. "Inflation-adjusted potential output," International Finance Discussion Papers 561, Board of Governors of the Federal Reserve System (U.S.).
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