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
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.
- 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,
- 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
- 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):
- Engle, R. (1974). "Band spectrum regression." International Economic Review,
- 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
- 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
- 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,
- Priestley, M. (1996). "Wavelets and
time-dependent spectral analysis." Journal of Time Series Analysis,
- 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."
- 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,
- 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.