Skip to main content
Article thumbnail
Location of Repository

Narrow-band analysis of nonstationary processes.

By D. Marinucci and Peter M. Robinson

Abstract

The behavior of averaged periodograms and cross-periodograms of a broad class of nonstationary processes is studied. The processes include nonstationary ones that are fractional of any order, as well as asymptotically stationary fractional ones. The cross-periodogram can involve two nonstationary processes of possibly different orders, or a nonstationary and an asymptotically stationary one. The averaging takes place either over the whole frequency band, or over one that degenerates slowly to zero frequency as sample size increases. In some cases it is found to make no asymptotic difference, and in particular we indicate how the behavior of the mean and variance changes across the two-dimensional space of integration orders. The results employ only local-to-zero assumptions on the spectra of the underlying weakly stationary sequences. It is shown how the results can be applied in fractional cointegration with unknown integration orders.

OAI identifier: oai:RePEc:ner:lselon:http://eprints.lse.ac.uk/303/

Suggested articles

Citations

  1. (1987). A functional central limit theorem for fractional processes.
  2. (1999). Alternative forms of fractional Brownian motion.
  3. (1974). Asymptotic Behaviour of Trigonometric Series. Chinese Univ.,
  4. (1987). Asymptotic properties of least squares estimators of cointegrating vectors.
  5. (1993). Asymptotics for the low-frequency ordinates of the periodogram of a long-memory time series.
  6. (1997). Consistency of the averaged cross-periodogram in long memory series.
  7. (1991). Contributions to strong approximations in time series with applications in nonparametric statistics and functional central limit theorems.
  8. (1968). Convergence of Probability Measures.
  9. (1986). Discrimination between monotonic trends and long-range dependence.
  10. (1979). Distribution of the estimators for autoregressive time series with a unit root.
  11. (1998). Efficient estimation of cointegrating relationships among higher order and fractionally integrated processes. Banco de Espana–Servicio de Estudios, Documento de Trabajo 9617.
  12. (1997). Fitting time series models to nonstationary processes.
  13. (1995). Gaussian semiparametric estimation of long-range dependence.
  14. (1951). Hypothesis testing in time series analysis. Thesis,
  15. (1995). Inference for unstable long-memory processes with applications to fractional unit root autoregressions.
  16. (1986). Large-sample properties of parameter estimates for strongly dependent stationary Gaussian time series.
  17. (1995). Log-periodogram regression of time series with long-range dependence.
  18. (1985). Non-central limit theorems for quadratic forms in random variables having long-range dependence.
  19. (2001). On asymptotic inference in cointegrated time series with fractionally integrated errors.
  20. (1963). On spectral analysis with missing observations and amplitude modulation.
  21. (1996). Parameter estimation for infinite variance fractional ARIMA.
  22. (1994). Rates of convergence and optimal spectral bandwidth for long-range dependence.
  23. (1963). Regression for time series with errors of measurement.
  24. (1994). Semiparametric analysis of long-memory time series.
  25. (1997). Semiparametric frequency-domain analysis of fractional cointegration.
  26. (2000). Spectral regression for cointegrated time series with long-memory innovations.
  27. (1991). Spectral regression for cointegrated time series.
  28. (1987). Statistical aspects of self-similar processes.
  29. (1976). The asymptotic distribution of serial covariances.
  30. (2000). The averaged periodogram for nonstationary vector time series. Statist. Inference Stochastic Process.
  31. (1983). The estimation and application of long memory time series models.
  32. (1990). The fractional unit root distribution.
  33. (1971). Time Series Analysis. Forecasting and Control. HoldenDay,
  34. (1975). Time Series, Data Analysis and Theory.
  35. (1977). Trigonometric Series. Cambridge Univ. Press. London School of Economics Houghton Street London WC2A 2AE United Kingdom E-mail: p.m.robinson@lse.ac.uk
  36. (2000). Weak convergence of multivariate fractional processes. Stochastic Process.

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.