DOI QR코드

DOI QR Code

Consistency of the Periodogram When the Long-Run Variance is Degenerate

  • Lee, Jin (Department of Economics, Ewha Womans University)
  • Received : 2011.12.08
  • Accepted : 2012.02.27
  • Published : 2012.03.31

Abstract

Sample periodogram is widely known as an inconsistent estimator for true spectral density. We show that it becomes consistent when the true spectrum at the zero frequency (often known as long-run variance) equals zero. Asymptotic results for consistency of the periodogram as well as the rate of convergence are formally derived.

Keywords

References

  1. Andrews, D. W. K. (1991). Heteroskedasticity and autocorrelation consistent covariance matrix estimation, Econometrica, 59, 817-858. https://doi.org/10.2307/2938229
  2. Brockwell, P. and Davis, R. (1990). Time Series: Theory and Methods, Springer series in statistics.
  3. Granger, C. (1969). Investigating causal relations by econometric models and cross-spectral methods, Econometrica, 37, 315-340.
  4. Hamilton, J. (1994). Time Series Analysis, Princeton.
  5. Lee, J. (2010). Long-run variance estimation for linear processes under possible degeneracy, Journal of Economic Theory and Econometrics, 21, 1-22.
  6. Newey, W. and West, K. (1994). Automatic lag selection in covariance matrix estimation, Review of Economic Studies, 61, 631-653. https://doi.org/10.2307/2297912
  7. Phillips, P. C. B. (2005). HAC estimation by automated regression, Econometric Theory, 21, 116-142.
  8. Priestley, M. B. (1981). Spectral Analysis and Time Series, Academic Press New York.
  9. Saikkonen and Lukkonen (1993). Testing for moving average unit root in autoregressive integrated moving average unit root, Journal of the American Statistical Association, 88, 596-601. https://doi.org/10.1080/01621459.1993.10476312