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The empirical distribution of sequential LS factors in Multi-level Dynamic Factor Models

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  • Bellocca, Gian Pietro Enzo
  • Garrón Vedia, Ignacio
  • Rodríguez Caballero, Carlos Vladimir
  • Ruiz Ortega, Esther

Abstract

The research question we answer in this paper is whether the asymptotic distribution derived by Bai (2003) for Principal Components (PC) factors in dynamic factor models (DFMs) can approximate the empirical distribution of the sequential Least Squares (SLS) estimator of global and group-specific factors in multi-level dynamic factor models (ML-DFMs). Monte Carlo experiments confirm that under general forms of the idiosyncratic covariance matrix, the finite-sample distribution of SLS global and group-specific factors can be well approximated using the asymptotic distribution of PC factors. We also analyse the performance of alternative estimators of the asymptotic mean squared error (MSE) of the SLS factors and show that the MSE estimator that allows for idiosyncratic cross-sectional correlation and accounts for estimation uncertainty of factor loadings is best.

Suggested Citation

  • Bellocca, Gian Pietro Enzo & Garrón Vedia, Ignacio & Rodríguez Caballero, Carlos Vladimir & Ruiz Ortega, Esther, 2026. "The empirical distribution of sequential LS factors in Multi-level Dynamic Factor Models," DES - Working Papers. Statistics and Econometrics. WS 49336, Universidad Carlos III de Madrid. Departamento de Estadística.
    • Handle: RePEc:cte:wsrepe:49336
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    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: 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
    • F47 - International Economics - - Macroeconomic Aspects of International Trade and Finance - - - Forecasting and Simulation: Models and Applications

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