Modern Spectrum Methods in Time Series Analysis: Physical Science, Environmental Science and Computer Modeling

Why Study Time Series?

Time is an important factor in the recording of data. In a time series, where a sequence of data points are collected over an interval of time, time is the significant variable.

Natural time series in geophysics and solar physics often have complex stochastic structures and spectra with “many lines”. These are not generally captured by low-order parametric models. 

“Many line” problems were first discovered while searching for causes of problems in engineering systems. These were associated with the active solar maximum around 1990, leading to advances in robust spectral estimation. 

The large number of periodic components in time series highlights the importance of modeling for physical understanding and for careful statistical characterization. 

Areas of Exploration

Time Series Analysis

Includes data analysis of time series using multi-taper and related methods. In addition to extracting information from natural time series, spectral estimation methods will be explored for the output of multi-fidelity computer models.

Data Applications

Includes envisaging applications to models of seismic “noise” background, solar gravity modes, environmental solar effects, pollutants and meteorological phenomena.

Modern Spectrum Methods

Includes developing methods to model processes with features such as: nearly periodic components, nonlinear coupling, non-stationarity and non-Gaussian distributions. This is done to devise appropriate statistical tests for their frequency domain parameters.

Solving Global Challenges

Research Team’s Goal

To develop modern methods for the exploratory data analysis of time series, with the help of international collaborations.