Modeling and estimation of stochastic volatility: application to inflation

Abstract

This study presents a detailed analysis of the modeling of stochastic volatility (SVM) applied to the inflation series of Greater Buenos Aires, Argentina, covering the period from January 1943 to May 2019. Using state-space models and estimation techniques based on the Kalman filter and smoother, the paper proposes an alternative and more flexible approach than traditional ARCH-GARCH models. In SVMs, volatility depends on its own past values rather than on the returns of the series. A specific model is developed that captures the key characteristics of the inflation series, including unobservable components that are estimated and modeled over time. This approach allows for the decomposition of inflation into structural components such as core inflation (which excludes volatile sectors like food and energy) and trend inflation (which includes core inflation plus the remaining sectors). Additionally, an in-depth analysis of the 2004-2015 period is conducted, when the National Institute of Statistics and Censuses (INDEC) was politically intervened, demonstrating how the intervention impacted the accuracy and reliability of the reported data. The results show that the SVM model is capable of capturing volatility dynamics in a complex economic time series like inflation, providing better estimates and forecasts than ARCH-GARCH models in contexts of high variability and structural changes. In particular, the state-space approach enables the estimation of the stochastic volatility of errors, revealing key insights into inflation cycles and systematic errors in the data reported by INDEC. Furthermore, the theoretical implications of these findings for the Argentine economy and their relevance for modeling volatile economic time series are discussed.