  The disaggregated time-series data for Consumer Price Index often exhibits
frequent instances of exact zero price changes, stemming from measurement
errors inherent in the data collection process. However, the currently
prominent stochastic volatility model of trend inflation is designed for
aggregate measures of price inflation, where exact zero price changes rarely
occur. We propose a zero-inflated stochastic volatility model applicable to
such nonstationary real-valued multivariate time-series data with exact zeros,
by a Bayesian dynamic generalized linear model that jointly specifies the
dynamic zero-generating process. We also provide an efficient custom Gibbs
sampler that leverages the P\'olya-Gamma augmentation. Applying the model to
disaggregated Japanese Consumer Price Index data, we find that the
zero-inflated model provides more sensible and informative estimates of
time-varying trend and volatility. Through an out-of-sample forecasting
exercise, we find that the zero-inflated model provides improved point
forecasts when zero-inflation is prominent, and better coverage of interval
forecasts of the non-zero data by the non-zero distributional component.
