The Decomposition of Economic Relationships by Time Scale Using Wavelets - Abstract

The Decomposition of Economic Relationships by Time Scale Using Wavelets: Expenditure and Income

James B. Ramsey and Camille Lampart
Department of Economics
New York University


Pages 23-42

Abstract

Economists have long known that time scale matters, in that the structure of decisions as to the relevant time horizon, degree of time aggregation, strength of relationship, and even the relevant variables differ by time scale. Unfortunately, until recently it was difficult to decompose economic time series into orthogonal time-scale components except for the short and long run, in which the former is dominated by noise. This paper uses wavelets to produce an orthogonal decomposition of some economic variables by time scale over six different time scales. The relationship of interest is the permanent income hypothesis. We confirm that time-scale decomposition is very important for analyzing economic relationships and that a number of anomalies previously noted in the literature are explained by these means. The analysis indicates the importance of recognizing variations in phase between variables when investigating the economic relationships.

Bibliography

  • Brillinger, David R. (1994). "Uses of cumulants in wavelet analysis." Proceedings of SPIE Conference on Advanced Signal Processing , 2296: 2-18.
  • Bruce, A., and H. Gao (1994). S+WAVELETS User's Manual Version 1.0 . Seattle, WA: MathSoft, Inc., StatSci Division, Mktg@StatSci.com.
  • Campbell, J. Y., and N. G. Mankiw (1989). "Consumption, income, and interest rates: Reinterpreting the times series evidence." NBER Macroeconomics Annual 1989 . Cambridge, MA: NBER.
  • Campbell, J. Y., and N. G. Mankiw (1990). "Permanent income, current income and consumption." Journal of Business & Economic Statistics , 8(3):265-279.
  • Christiano, L. J., M. Eichenbaum, and D. Marshall (1991). "The permanent income hypothesis revisited." Econometrica , 59(2):397-423.
  • Chui, C. K. (1992). An Introduction to Wavelets . San Diego, CA: Academic Press.
  • Corbae, D., S. Ouliaris, and P. C. Phillips (1991). "A reexamination of the consumption function using frequency domain regressions." Department of Economics Working Paper Series 91-25, University of Iowa.
  • Daubechies, I. (1992). Ten Lectures on Wavelets, CBMS-NSF Regional Conference Series on Applied Mathematics , vol. 61. Philadelphia, PA: Society for Industrial and Applied Mathematics.
  • Deaton, A. S. (1987). "Life-cycle models of consumption: Is the evidence consistent with the theory?" In T. F. Bewley (ed.) Advances in Econometrics: Fifth World Congress , vol. 2. New York: Cambridge University Press.
  • Donoho, D., I. Johnstone, G. Kerkyacharian, and D. Picard (1995). "Wavelet shrinkage: Asymptopia (with discussion)?" Journal of the Royal Statistical Society Series B (Methodological) , 57(2): 301-369.
  • Engle, R. (1974). "Band spectrum regression." International Economic Review , 15(1): 1-11.
  • Flavin, M. A. (1981). "The adjustment of consumption to changing expectations about future income." Journal of Political Economy , 89(5): 974-1009.
  • Friedman, M. (1957). A Theory of the Consumption Function . Princeton, NJ: Princeton University Press.
  • Friedman, M. (1963). "Windfalls, the 'horizon,' and related concepts in the permanent-income hypothesis." In Carl Christ, et al. (eds.), Measurement in Economics: Studies in Mathematical Economics and Econometrics in Memory of Yehuda Grunfeld . Stanford, CA: Stanford University Press, pp. 3-28.
  • Gilbert, S. (1995). "Structural change: Estimation and testing by wavelet regression." Mimeograph, University of California at San Diego.
  • Goffe, W. L. (1994). "Wavelets in macroeonomics: An introduction." In D. Belsley (ed.), Computational Techniques for Econometrics and Economic Analysis . The Netherlands: Kluwer Academic, pp. 137-149.
  • Greenblatt, Seth A. (1996). "Atomic decomposition of financial data." Working Paper, Center for Quantitative Economics and Computing, Department of Economics, University of Reading, UK.
  • Grossman, S. J., and G. Laroque (1989). "Asset pricing and optimal portfolio choice in the presence of illiquid consumption goods." Econometrica , 59:1221-1248.
  • Hall, R. E. (1978). "Stochastic implications of the life cycle-permanent income hypothesis: Theory and evidence." Journal of Political Economy , 86(61):971-987.
  • Hog, Esben (1996). "Fractional integration: A wavelet analysis approach." Working Paper, Department of Information Science, The Aarhus School of Business, Denmark.
  • Jensen, Mark J. (1996). "An alternative maximum likelihood estimator of long memory processes using compactly supported wavelets." Working Paper, Department of Economics, Southern Illinois University at Carbondale.
  • Molana, H. (1991). "The time series consumption function: Error correction, random walk and the steady state." The Economic Journal , 101:382-403.
  • Nelson, C. R. (1987). "A reappraisal of recent tests of the permanent income hypothesis." Journal of Political Economy , 95(3):641-646.
  • Priestley, M. (1996). "Wavelets and time-dependent spectral analysis." Journal of Time Series Analysis , 17(1):85-103.
  • Quah, Dennis (1990). "Permanent and transitory movements in labor income: An explanation for 'excess smoothness' in consumption." Journal of Political Economy , 98(3):449-475.
  • Ramsey, James B., and Camille Lampart (1997a). "The decomposition of economic relationships by time scale using wavelets." Working Paper 97-08, C. V. Starr Center, New York University.
  • Ramsey, James B., and Camille Lampart (1998). "The decomposition of economic relationships by time scale using wavelets: Money and income." Macroeconomic Dynamics , 2:49-71.
  • Ramsey, J. B., D. Usikov, and G. M. Zaslavsky (1995). "An analysis of U.S. stock price behavior using wavelets." Fractals , 3(2):377-389.
  • Ramsey, J. B., and Z. Zhang (1995). "The analysis of foreign exchange data using waveform dictionaries." Conference on High Frequency Dynamics . Zurich: Olsen and Associates.
  • Ramsey, J. B., and Z. Zhang (1996). "The application of wave form dictionaries to stock market index data." In J. Kadtke and Y. A. Kravtsov (eds.), Predictability of Complex Dynamical Systems . New York: Springer-Verlag, pp. 189-205.
  • Rioul, Olivier, and M. Vetterli (1991). "Wavelets and signal processing." IEEE Signal Processing Magazine , (October):14-38.
  • Strang, Gilbert (1989). "Wavelets and dilation equations." Siam Review , 31:613-627.
  • Truong, Young K., and Patil, Prakesh (1991). "On estimating possibly discontinuous regressions involving stationary time series." Working Paper, Department of Biostatistics, University of North Carolina at Chapel Hill.
  • Viard, A. D. (1993). "The productivity slowdown and the savings shortfall: A challenge to the permanent income hypothesis." Economic Inquiry , 31:549-563.
  • Wang, Yazhen (1995). "Jump and sharp cusp detection by wavelets." Biometrika , 82:385-397.