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Abstract:
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Joan Staniswalis’ work in the 1990s and late 1980s on local and adaptive methods for nonparametric estimation introduced many of the fundamental ideas and techniques driving analyses in this age of big and complex data. Motivated by problems in biology and environmental science, two of Joan’s passions, we build upon her work and discuss an adaptive nonparametric approach to multivariate time-varying power spectrum analysis. The procedure adaptively partitions a time series into an unknown number of approximately stationary segments, where some spectral components may remain unchanged across segments, allowing components to evolve differently over time. Local spectra within segments are fit through Whittle likelihood-based penalized spline models of modified Cholesky components. The approach is formulated in a Bayesian framework, in which the number and location of partitions are random, and relies on reversible jump Markov chain and Hamiltonian Monte Carlo methods that can adapt to the unknown number of segments and parameters.
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