Abstract
The entire discussion so far has been conducted within the following framework: A population was postulated and was asserted to be characterized by a density function whose parameters were unknown but fixed. We had at our disposal, a sample of size T (typically a random sample) from the population and on the basis of this sample we sought to make inferences regarding the unknown parameters. Generally we had used, at most, the second moment characteristics of the sample. Occasionally the analysis of (properties of) random variables in terms of moments of their distribution is said to be analysis “in the time domain”.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bartlett, M. S., “Periodogram Analysis and Continuous Spectra,” Biometrika, vol. 37 1950, pp. 1–16.
Bingham, C., M. Godfrey, and J. W. Tukey, “Modern Techniques of Power Spectrum Estimation,” IEEE Trans, on Audio and Electroacoustics, June 1962, pp. 55–66.
Blackman, R., and J. W. Tukey, The Measurement of Power Spectra, New York, Dover Publications, 1959.
Brandes, O., J. Farley, M. Hinich, and V. Zackrisson, “The Time Domain and the Frequency Domain in Time Series Analysis,” The Swedish Journal of Economics, vol. 70, 1968, pp.25–49.
Cramer, H., Mathematical Methods of Statistics, Princeton, N.J., Princeton University Press, 1946.
Davis, H. T., The Analysis of Economic Time Series, Cowles Foundation Monograph No. 6, Bloomington, Indiana, Principia Press, 1941. A detailed but rather dated study on economic time series.
Doob, J. L., Stochastic Processes, New York, Wiley, 1952.
Goodman, N. R., “Some Comments on Spectral Analysis of Time Series,” Technometrics, vol. 3, 1961, pp. 221–228.
Grenander, U., and M. Rosenblatt, Statistical Analysis of Stationary Time Series, New York, Wiley, 1957.
Hannan, E. J., “The Estimation of the Spectral Density After Trend Removal,” Journal of the Royal Statistical Society (Series B), vol. 20, 1958, pp. 323–333.
Hannan E. J., Times Series Analysis, London, Methuen & Co., and New York, Wiley, 1960.
Hinich, M. J., and J. U. Farley, “Theory and Application of an Estimation Model for Nonstationary Time Series Means,” Management Science, vol. 12, 1966, pp. 648–658.
Jenkins G. M., “General Considerations in the Estimation of Spectra,” Techometrics, vol. 3, 1961, pp. 133–166.
Kendall, M. G., Contributions to the Study of Oscillatory Time Series, Cambridge, Cambridge University Press, 1946.
Kendall, M. G., and A. Stuart, The Advanced Theory of Statistics, New York, Hafner Publishing Co., 1966. Chapter 49 deals with spectral theory.
Parzen, E., “On Consistent Estimates of the Spectrum of a Stationary Time Series,” Annals of Mathematical Statistics, vol. 28, 1957, pp. 329–348.
Parzen, E., “Mathematical Considerations in the Estimation of Spectra,” Technometrics, vol. 3, 1961, pp. 167–190.
Parzen, E. Stochastic Processes, San Francisco, Holden-Day, 1962.
Parzen, E., “Notes on Fourier Analysis and Spectral Windows,” unpublished paper, U.S Office of Naval Research, Dept. of the Navy, 1962.
Parzen, E., “The Role of Spectral Analysis in Time Series,” Technical Report No. 2, Department of Statistics, Stanford University, 1965.
Schuster, A., “On the Investigation of Hidden Periodicities with Application to a Supposed 26-Day Period of Meteorological Phenomena,” Terrestrial Magnetism, vol. 3, 1898, pp. 13–41.
Slutzsky, E., “The Summation of Random Causes as the Source of Cyclic Processes,” Econometrica, vol. 5, 1937, pp. 105–147.
Tukey, J. W., “Discussion Emphasizing the Connection Between Analysis of Variance and Spectrum Analysis,” Technometrics, vol. 3, pp. 191–219.
Wold, H., A Study in the Analysis of Stationary Time Series, Uppsala, Sweden, University of Uppsala, 1938.
Yaglom, A. N., An Introduction to the Theory of Stationary Random Functions, Englewood Cliffs, N.J., Prentice Hall, 1962. Part 1 gives a comprehensive discussion of spectral theory.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1974 Springer-Verlag New York Inc
About this chapter
Cite this chapter
Dhrymes, P.J. (1974). Spectral Analysis. In: Econometrics. Springer Study Edition. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-9383-2_9
Download citation
DOI: https://doi.org/10.1007/978-1-4613-9383-2_9
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-90095-7
Online ISBN: 978-1-4613-9383-2
eBook Packages: Springer Book Archive