The Cross-Wavelet Transform and Analysis of Quasiperiodic Behavior in the Pearson-Readhead VLBI Survey Sources

The Astrophysical Journal (Impact Factor: 6.28). 12/2002; DOI: 10.1086/375511
Source: arXiv

ABSTRACT We introduce an algorithm for applying a cross-wavelet transform to analysis of quasiperiodic variations in a time-series, and introduce significance tests for the technique. We apply a continuous wavelet transform and the cross-wavelet algorithm to the Pearson-Readhead VLBI survey sources using data obtained from the University of Michigan 26-m parabloid at observing frequencies of 14.5, 8.0, and 4.8 GHz. Thirty of the sixty-two sources were chosen to have sufficient data for analysis, having at least 100 data points for a given time-series. Of these thirty sources, a little more than half exhibited evidence for quasiperiodic behavior in at least one observing frequency, with a mean characteristic period of 2.4 yr and standard deviation of 1.3 yr. We find that out of the thirty sources, there were about four time scales for every ten time series, and about half of those sources showing quasiperiodic behavior repeated the behavior in at least one other observing frequency. Comment: Revised version, accepted by ApJ. 17 pages, 13 figures, color figures included as gifs, seperate from the text. The addition of statistical significance tests has resulted in modifying the technique and results, but the broad conclusion remain the same. A high resolution version may be found at

  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: The cyclical components of time series data have been typically examined with the use of spectral analysis or ARMA models. While spectral analysis allows direct estimation of which frequencies play relevant roles in explaining time series variance, ARMA models are a time domain approach that also allows the indirect detection of those cycles. What they also share, however, is both an assumption of stationarity and of the time invariance of the cycles they uncover. Unfortunately, many economic and political time-series are, in fact, noisy, complex and strongly non-stationary. And most importantly, it is probably unwise to assume, especially over prolonged periods of time, that the underlying processes generating the time series data we observe are themselves time invariant. Wavelet analysis helps overcoming these problems in the analysis of the cyclical components of a time series and of the frequencies that explain its variance. It performs the estimation of the spectral characteristics of a time-series as a function of time, revealing how the different periodic components of the time-series change over time. In this paper, we present three tools that, to our knowledge, have not yet been used by political scientists - the wavelet power spectrum, the cross-wavelet coherency and the phase difference - as well as a metric to compare different wavelet spectra. We apply these tools to the study of presidential election cycles in the United States.
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: Stirling et al. recently reported the discovery of a 2.3 yr periodic variation in the structural position angle of the parsec-scale radio core in the blazar BL Lac. We searched for independent confirmation of this periodic behavior using 43 GHz images of the radio core during 10 epochs overlapping those of Stirling et al. Our maps are consistent with several periodicities, including one near the period reported by Stirling et al. By comparing our position angle measurements with those of Stirling et al., we find strong, consistent evidence for position angle variations of the inner core during the observed epochs. However, the claim of periodic variation is not convincing, especially when the most recent epochs (2000.60–2003.78) are included. A definitive resolution will require continued monitoring of the core structure over several periods.
    The Astrophysical Journal 04/2005; 623. · 6.28 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: Central banks have different objectives in the short and long run. Governments operate simultaneously at different timescales. Many economic processes are the result of the actions of several agents, who have different term objectives. Therefore, a macroeconomic time series is a combination of components operating on different frequencies. Several questions about economic time series are connected to the understanding of the behavior of key variables at different frequencies over time, but this type of information is difficult to uncover using pure time-domain or pure frequency-domain methods. To our knowledge, for the first time in an economic setup, we use cross-wavelet tools to show that the relation between monetary policy variables and macroeconomic variables has changed and evolved with time. These changes are not homogeneous across the different frequencies. c 2008 Elsevier B.V. All rights reserved.

Full-text (2 Sources)

Available from
May 21, 2014