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.

翻译：细项居民消费价格指数的时间序列数据中，常因数据采集过程的测量误差而频繁出现价格变动恰好为零的情形。然而，当前主流的趋势通胀随机波动模型适用于以汇总指标衡量的价格通胀——此类情境下价格变动恰好为零的情形极少发生。本文提出一种适用于含确切零值的非平稳实值多元时间序列数据的零膨胀随机波动模型，通过贝叶斯动态广义线性模型联合刻画动态零值生成过程。我们还设计了一种利用Pólya-Gamma增广技术的高效定制Gibbs抽样算法。将该模型应用于日本细项居民消费价格指数数据后，我们发现零膨胀模型能更合理且更有效地估计时变趋势与波动性。通过样本外预测检验，我们发现在零通胀显著的场景下，零膨胀模型能改进点预测精度，且其非零分布成分能为非零数据的区间预测提供更优的覆盖效果。