Zero-inflated stochastic volatility model for disaggregated inflation data with exact zeros

Abstract

The disaggregated time-series for the Consumer Price Index (CPI) often exhibits exact zero price changes, stemming from structural features of the data collection process. However, the currently prominent stochastic volatility model of trend-inflation is designed for aggregate measures of price inflation, where zeros rarely occur. We formulate a zero-inflated stochastic volatility model applicable to such non-stationary, real-valued, multivariate time-series data with exact zeros, which jointly specifies the dynamic zero-generating process. For posterior inference, an efficient custom Pólya--Gamma augmented Gibbs sampler is derived. Applying the model to disaggregated CPI data in four advanced economies -- US, UK, Germany, and Japan -- we find that the zero-inflated model yields more informative estimates of time-varying trend and volatility, as it accounts for the presence of zeros and avoids underestimation. In an out-of-sample forecasting exercise, we find that the zero-inflated model delivers improved point forecasts and better calibrated interval forecasts, particularly when zero-inflation is prevalent.

Figures (12)

• Figure 1: Time-series plot of the electricity component for three selected countries. The comparison highlights: (1) occurrences of exact zeros, (2) heterogeneity in the frequency and persistence of zeros, (3) non-stationarity in the non-zero component, and (4) missing values prior to component-level data collection. Definition: Inflation (top) is defined as the quarterly % change in CPI (bottom) from the previous quarter. Note: Gray shaded vertical bands indicate periods of observed price staleness.
• Figure 2: Heatmap of zero and missing-data patterns in the inflation time-series. zero-inflation and missing observations are prevalent features of disaggregated CPI inflation data, largely due to the mode of data collection.
• Figure 3: Heatmap of the empirical component-pairwise correlation matrix, including both zero and non-zero observations. The empirical correlation reinforces the necessity of modeling inter-component dependencies when estimating trend inflation and volatility.
• Figure 4: Top: Time-series of electricity inflation in Japan. Solid blue line: posterior mean estimate of the trend. Red shaded region: posterior mean estimate of the time-varying standard deviation around the trend, $\pm\exp(h_t/2)$; stochastic volatility estimate. Bottom, solid green line: posterior mean estimate of time-varying probability of zero. Green shaded region: 90% credible interval.
• Figure 5: Inflation time-series of games of chance in Germany, and posterior estimates of the trend (solid blue line), predictive mean (dotted black line), marginal time-varying volatility in standard deviation (solid red line), and probability of zero (solid green line). Shaded regions: 90% credible interval.