Title: Wavelets in Analysis of Climate Time Series
Abstract: Wavelets are a particularly useful tool in statistical analyses of time series. Their multi-resolution property provides an advantage over the windowed Fourier transformation, allowing for extractions of larger signal patterns and, when necessary, focus on fine details of the signal. Moreover, the discrete wavelet transformation is O(n) which is faster than the fast Fourier transform. Meanwhile, wavelet coefficients maintain similar properties to Fourier coefficients. Thus, with the spatial and temporal relationships prevalent in climate data, these constructs are a natural choice in analyses. During this short course, participants will be introduced to basic statistical theory surrounding the discrete wavelet transformation of time series. We will present traditional as well as recent approaches using wavelets for signal extraction from time series. Participants should bring a laptop, preferably with R installed, for a hands-on data analysis experience. By the end of the workshop, all participants will have analyzed a real climate dataset with the help of the discrete wavelet transformation.
Biography
Megan is currently an assistant professor in the Mathematics department at Rose-Hulman Institute of Technology. She graduated with a PhD in statistics from the School of Statistics at the University of Minnesota in 2016. Her research interests/specialties include nonparametric statistics, applications of wavelets in statistics, and development of statistical methods for climate data. She is an active R package developer and has expertise in methods for statistical education of STEM majors.
