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High-Dimensional Conditionally Gaussian State Space Models with Missing Data

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  • Joshua C. C. Chan
  • Aubrey Poon
  • Dan Zhu

Abstract

We develop an efficient sampling approach for handling complex missing data patterns and a large number of missing observations in conditionally Gaussian state space models. Two important examples are dynamic factor models with unbalanced datasets and large Bayesian VARs with variables in multiple frequencies. A key insight underlying the proposed approach is that the joint distribution of the missing data conditional on the observed data is Gaussian. Moreover, the inverse covariance or precision matrix of this conditional distribution is sparse, and this special structure can be exploited to substantially speed up computations. We illustrate the methodology using two empirical applications. The first application combines quarterly, monthly and weekly data using a large Bayesian VAR to produce weekly GDP estimates. In the second application, we extract latent factors from unbalanced datasets involving over a hundred monthly variables via a dynamic factor model with stochastic volatility.

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  • Joshua C. C. Chan & Aubrey Poon & Dan Zhu, 2023. "High-Dimensional Conditionally Gaussian State Space Models with Missing Data," Papers 2302.03172, arXiv.org.
  • Handle: RePEc:arx:papers:2302.03172
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    Cited by:

    1. Mertens, Elmar, 2023. "Precision-based sampling for state space models that have no measurement error," Journal of Economic Dynamics and Control, Elsevier, vol. 154(C).
    2. Luca Barbaglia & Lorenzo Frattarolo & Niko Hauzenberger & Dominik Hirschbuehl & Florian Huber & Luca Onorante & Michael Pfarrhofer & Luca Tiozzo Pezzoli, 2024. "Nowcasting economic activity in European regions using a mixed-frequency dynamic factor model," Papers 2401.10054, arXiv.org.
    3. Joshua Chan, 2023. "BVARs and Stochastic Volatility," Papers 2310.14438, arXiv.org.

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    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C55 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Large Data Sets: Modeling and Analysis

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