Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-23T08:11:53.079Z Has data issue: false hasContentIssue false
  • English
  • Français

Quantile spectral analysis and long-memory time series

Published online by Cambridge University Press:  14 July 2016

Emanuel Parzen
Get access Rights & Permissions [Opens in a new window]

Abstract

An approach to time series model identification is described which involves the simultaneous use of frequency, time and quantile domain algorithms; the approach is called quantile spectral analysis. It proposes a framework to integrate the analysis of long-memory (non-stationary) time series with the analysis of short-memory (stationary) time series.

Keywords

MODEL IDENTIFICATIONQUANTILE DATA ANALYSISHURST EXPONENTSPECTRAL INDEX OF REGULAR VARIATION
Type
Part 1—Structure and General Methods for Time Series
Information
Journal of Applied Probability , Volume 23 , Issue A: Essays in Time Series and Allied Processes , 1986 , pp. 41 - 54
Copyright
Copyright © 1986 Applied Probability Trust 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Akaike, H. (1977) On entropy maximization principle. In Applications of Statistics , ed. Krishnaiah, P. R., North Holland, Amsterdam, 27–41.Google Scholar
Bhattacharya, R. N., Gupta, V. K. and Waymire, E. (1983) The Hurst effect under trends. J. Appl. Prob. 20, 649–662.Google Scholar
Box, G. E. P. and Jenkins, G. M. (1970) Time Series Analysis, Forecasting, and Control. Holden Day, San Francisco.Google Scholar
Cox, D. R. (1984) Long-range dependence: a review. In Statistics: An Appraisal , ed. David, H. A. and David, H. T., Iowa State University Press, Ames, 55–74.Google Scholar
Freedman, L. and Lane, D. (1981) The empirical distribution of the Fourier coefficients of a sequence of independent, identically distributed long-tailed random variables. Z. Wahrscheinlichkeitsth. 55, 21–37.CrossRefGoogle Scholar
Geweke, J. and Porter-Hudak, S. (1983) The estimation and application of long memory time series models. J. Time Series Analysis. 4, 221–238.Google Scholar
Granger, C. W. G. and Joyeux, R. (1980) An introduction to long memory time series models and fractional differencing. J. Time Series Analysis 1, 15–29.Google Scholar
Hannan, E. J. (1970) Multiple Time Series. Wiley, New York.Google Scholar
Hannan, E. J. and Kanter, M. (1977) Autoregressive processes with infinite variance. J. Appl. Prob. 14, 411–415.Google Scholar
Hosking, J. R. M. (1981) Fractional differencing. Biometrika 68, 165–176.Google Scholar
Janacek, G. J. (1982) Determining the degree of differencing for time series via the log spectrum. J. Time Series Analysis 3, 177–183.Google Scholar
Mandelbrot, B. (1973) Statistical methodology for nonperiodic cycles: from the covariance to R/S analysis. Rev. Econom. Social Measurement , 259–290.Google Scholar
Mandelbrot, B. (1982) The Fractal Geometry of Nature. Freeman, San Francisco.Google Scholar
Mandelbrot, B. and Taqqu, M. (1979) Robust R/S analysis of long run serial correlation. 42nd Internat. Statist. Inst., Manila , 1–38.Google Scholar
Mandelbrot, B. and Wallis, J. (1968) Noah, Joseph and operational hydrology. Water Resources Res. 4, 909–918.Google Scholar
Parzen, E. (1979) Nonparametric statistical data modeling (with discussion), J. Amer. Statist. Assoc. 74, 105–131.Google Scholar
Parzen, E. (1981) Time series model identification and prediction variance horizon. In Applied Time Series Analysis II , ed. Findley, David F., Academic Press, New York, 415–447.Google Scholar
Parzen, E. (1982) ARARMA models for time series analysis and forecasting. J. Forecasting 1, 67–82.CrossRefGoogle Scholar
Parzen, E. (1982) Maximum entropy interpretation of autoregressive spectral densities. Statist. Prob. Letters , 1, 2–6.Google Scholar
Rosenblatt, M. (1981) Limit theorems for Fourier transforms of functionals of Gaussian sequences. Z. Wahrscheinlichkeitsth. 55, 123–132.Google Scholar