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Normality tests for latent variables

Author

Listed:
  • Martín Almuzara
  • Dante Amengual
  • Enrique Sentana

Abstract

We exploit the rationale behind the Expectation Maximization algorithm to derive simple to implement and interpret LM normality tests for the innovations of the latent variables in linear state space models against generalized hyperbolic alternatives, including symmetric and asymmetric Student ts. We decompose our tests into third and fourth moment components, and obtain one‐sided likelihood ratio analogues, whose asymptotic distribution we provide. When we apply our tests to a common trend model which combines the expenditure and income versions of US aggregate real output to improve its measurement, we reject normality if the sample period extends beyond the Great Moderation.

Suggested Citation

  • Martín Almuzara & Dante Amengual & Enrique Sentana, 2019. "Normality tests for latent variables," Quantitative Economics, Econometric Society, vol. 10(3), pages 981-1017, July.
    • Handle: RePEc:wly:quante:v:10:y:2019:i:3:p:981-1017
    DOI: 10.3982/QE859
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    Cited by:

    1. Amengual, Dante & Fiorentini, Gabriele & Sentana, Enrique, 2025. "Information matrix tests for multinomial logit models," Economics Letters, Elsevier, vol. 247(C).
    2. Demetrescu, Matei & Kruse-Becher, Robinson, 2025. "Is U.S. real output growth non-normal? A tale of time-varying location and scale," Journal of Economic Dynamics and Control, Elsevier, vol. 171(C).
    3. Martín Almuzara & Gabriele Fiorentini & Enrique Sentana, 2023. "Aggregate Output Measurements: A Common Trend Approach," Advances in Econometrics, in: Essays in Honor of Joon Y. Park: Econometric Methodology in Empirical Applications, volume 45, pages 3-33, Emerald Group Publishing Limited.
    4. Dante Amengual & Gabriele Fiorentini & Enrique Sentana, 2022. "Moment tests of independent components," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 13(1), pages 429-474, May.
    5. Amengual, Dante & Bei, Xinyue & Carrasco, Marine & Sentana, Enrique, 2025. "Score-type tests for normal mixtures," Journal of Econometrics, Elsevier, vol. 248(C).
    6. Dante Amengual & Gabriele Fiorentini & Enrique Sentana, 2022. "Tests for Random Coefficient Variation in Vector Autoregressive Models," Advances in Econometrics, in: Essays in Honour of Fabio Canova, volume 44, pages 1-35, Emerald Group Publishing Limited.
    7. Matei Demetrescu & Robinson Kruse-Becher, 2021. "Is U.S. real output growth really non-normal? Testing distributional assumptions in time-varying location-scale models," CREATES Research Papers 2021-07, Department of Economics and Business Economics, Aarhus University.
    8. Dante Amengual & Gabriele Fiorentini & Enrique Sentana, 2024. "The information matrix test for Gaussian mixtures," Working Papers wp2024_2401, CEMFI.
    9. Poncela, Pilar & Ruiz, Esther & Miranda, Karen, 2021. "Factor extraction using Kalman filter and smoothing: This is not just another survey," International Journal of Forecasting, Elsevier, vol. 37(4), pages 1399-1425.
    10. Dante Amengual & Gabriele Fiorentini & Enrique Sentana, 2025. "The information matrix test for Markov switching autoregressive models with covariate-dependent transition probabilities," Working Papers wp2025_2502, CEMFI.

    More about this item

    JEL classification:

    • 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
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • E01 - Macroeconomics and Monetary Economics - - General - - - Measurement and Data on National Income and Product Accounts and Wealth; Environmental Accounts

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