Stochastic Volatility for Ecological Momentary Assessment DataZhang, Gehui (2024) Stochastic Volatility for Ecological Momentary Assessment Data. Doctoral Dissertation, University of Pittsburgh. (Unpublished)
AbstractModels that treat the variance of a time series as a stochastic process, known as stochastic volatility models, have proven to be an important tool for analyzing dynamic variability. Current methods for fitting and conducting inference on stochastic volatility models are limited by the assumption that any missing data are missing at random. With a recent explosion in technology to facilitate the collection of dynamic self-response data for which mechanisms underlying missing data are inherently scientifically informative, this limitation in statistical methodology also limits scientific advancement. The broad goal of this dissertation is to develop the first statistical framework for modeling, fitting, and conducting inference on stochastic volatility with data that are missing not at random. Three specific methodologies are developed and explored within this framework. The first methodology focuses on the univariate stochastic volatility model with informative missingness. We propose a novel particle Gibbs method, which we refer to as the imputed conditional particle filter with ancestor sampling (ICPF-AS), in which the imputation of missing values is embedded into the particle sampler, and estimation of volatility accounts for the imputation. The method is illustrated through simulation studies and in the analysis of mobile phone self-reported mood from an individual who had suicide ideation and/or behavior in the past 4 months. The second methodology generalizes the parametric missing mechanism assumption in the first methodology to nonparametric missing mechanisms. By integrating the flexibility and adaptability of smoothing splines, this approach accommodates intricate relationships between missing indicators and variables of interest. Similar to the first methodology, the proposed method is evaluated through simulations and real data analysis. The third methodology extends the method developed for the univariate stochastic volatility model to the multivariate setting. Based on a multivariate dynamic factor model, we derive a multivariate ICPF-AS that can estimate the volatility processes related to idiosyncratic innovations and latent factors accounting for informative missingness. The proposed method is also illustrated through simulation studies and in the analysis of data from the motivation study. Share
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