A new class of structural time series models.
Wensheng Guo · Deep Blue (University of Michigan) · 1998
In this thesis, we present a sequence of univariate and multivariate structural time series models which have applications in many different fields, especially in analysis of biological signals. The first model sets up the general structure for a univariate time series with pulses and a smooth baseline. The structural parameters are treated as constants over time and their estimates are the summary statistics characterizing the features of the time series, such as pulse frequency, mean pulse amplitude, variance of pulse amplitude and decay rate. This model has a random effects interpretation, where the pulse locations and pulse amplitudes are modeled as random effects and estimated by their posterior estimates. The second model extends this framework into a bivariate setting where the structural parameters in one time series are modeled as functions of the history of the other series. As a result of this cross-related structure, we introduce a very flexible and robust probabilistic relationship which enables us to explore potential feedback relationships between hormones. The third model carries this idea one step further in a univariate setting by modeling the structural parameters of one series as functions of its own latent history. We extend the flexibility of the model by allowing the signal in the feedback system to differ from the one that we observe. All of these models allow flexible model structures, have clear interpretations for parameters and latent components and have a computationally efficient estimation procedure because of their conditionally Gaussian structures. These models are applied to several data sets from endocrinological studies to characterize hormone secretion and to explore feedback relationship in the biological regulating system.