This project studies novel inference procedures and models for seasonal time series. The results of this research will have direct impact on the diagnostics of seasonal adjustment procedures that are currently implemented at the U.S. Census Bureau and other domestic or foreign agencies where seasonal adjustments are routinely published. The "Visual Significance" method used at the Census Bureau lacks a rigorous statistical justification and the new spectral peak detection methods will help to quantify type I and II errors in a disciplined fashion for a wide class of processes. Although motivated by research problems at Census, the new methodology and models are expected to be useful in the analysis of time series from various disciplines, including economics, astronomy, environmental science, and atmospheric sciences, among others.
Specifically, the project consists of three interrelated parts. In the first part, the PI will develop two new methods of spectral peak detection, which are intended to provide more principled approaches to the "Visual Significance" method used at the U.S. Census Bureau. In the second part, the PI will address the band-limited goodness-of-fit testing using the integral of the square of the normalized periodogram. Instead of assuming the strong Gaussian-like assumption as done in the literature, the PI will use a new Studentizer, so that the limiting distribution of the self-normalization-based test statistic is pivotal under less stringent assumptions. In the third part, the PI will study a new parametric class of spectral density, which can be used in model-based seasonal adjustment to improve the quality of model fitting and seasonal adjustment. The new parametric models and related model-based seasonal adjustment, if successfully developed, may offer a more effective means of modeling and adjusting time series. The research will promote teaching and training through mentoring of undergraduate and graduate students and through the development of related lecture notes.
