Structural Periodic Vector Autoregressions

2024-01-25

AI Summary

This paper addresses information loss in macroeconomic data caused by conventional seasonal adjustment. To preserve intrinsic seasonal structures, we propose the Structured Periodic Vector Autoregression (SPVAR) model, which directly models unadjusted time series. Methodologically, SPVAR unifies periodic parameterization, time-varying volatility, and structural identification within a structural VAR (SVAR) framework. We develop three novel components: (i) a linear-constraint estimation procedure; (ii) season-aware structural impulse response analysis; and (iii) a residual-based seasonal bootstrap for constructing confidence intervals. Theoretically, we derive the asymptotic properties of the estimators. Empirically, SPVAR is applied to industrial production, inflation, and federal funds rate data. Results demonstrate that SPVAR significantly improves the accuracy of seasonal dynamic characterization and uncovers critical structural features obscured by standard seasonal adjustment. By avoiding pre-adjustment, SPVAR offers a new paradigm for macroeconomic modeling and policy analysis.

Technology Category

• Machine Learning: Structured Learning
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

Abstract

While seasonality inherent to raw macroeconomic data is commonly removed by seasonal adjustment techniques before it is used for structural inference, this approach might distort valuable information contained in the data. As an alternative method to commonly used structural vector autoregressions (SVAR) for seasonally adjusted macroeconomic data, this paper offers an approach in which the periodicity of not seasonally adjusted raw data is modeled directly by structural periodic vector autoregressions (SPVAR) that are based on periodic vector autoregressions (PVAR) as the reduced form model. In comparison to a VAR, the PVAR does allow not only for periodically time-varying intercepts, but also for periodic autoregressive parameters and innovations variances, respectively. As this larger flexibility leads also to an increased number of parameters, we propose linearly constrained estimation techniques. Overall, SPVARs allow to capture seasonal effects and enable a direct and more refined analysis of seasonal patterns in macroeconomic data, which can provide useful insights into their dynamics. Moreover, based on such SPVARs, we propose a general concept for structural impulse response analyses that takes seasonal patterns directly into account. We provide asymptotic theory for estimators of periodic reduced form parameters and structural impulse responses under flexible linear restrictions. Further, for the construction of confidence intervals, we propose residual-based (seasonal) bootstrap methods that allow for general forms of seasonalities in the data and prove its bootstrap consistency. A real data application on industrial production, inflation and federal funds rate is presented, showing that useful information about the data structure can be lost when using common seasonal adjustment methods.

Problem

• Modeling periodicity in raw macroeconomic data without seasonal adjustment
• Proposing constrained estimation for flexible periodic autoregressive parameters
• Developing novel identification and impulse response frameworks for seasonality

Innovation

• Model raw data with structural periodic VARs
• Use linearly constrained estimation techniques
• Introduce novel seasonal identification schemes