Published

2008-07-01

MODELO FACTORIAL DINÁMICO THRESHOLD

THRESHOLD DYNAMIC FACTOR MODEL

Keywords:

series de tiempo no lineales, análisis factorial, modelo threshold, algoritmo EM, filtro de Kalman (es)
Nonlinear time series, Factor analysis, Threshold model, EM algorithm, Kalman filter (en)

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Authors

  • María Elsa Correal Universidad de los Andes
  • Daniel Peña Universidad Carlos III de Madrid
En este artículo se introduce el modelo factorial dinámico threshold, el cual permite analizar sistemas de series temporales que presenten comportamientos no lineales del tipo umbral. Se propone un método de estimación que combina el algoritmo EM con un procedimiento de búsqueda directa utilizando los algoritmos del filtro y de suavización de Kalman. El procedimiento estima factores comunes con comportamientos que cambian de régimen de acuerdo con una variable umbral.
This paper introduces a threshold dynamic factor model for the analysis of vector time series which shows non-linear behavior of threshold type. We propose an estimation procedure combining an EM algorithm with a grid search procedure by the ways of the Kalman filter and smoothing recursions. We estimate common latent threshold factors that may explain the dynamic relationships within the group of variables.

Modelo factorial dinámico threshold

Threshold Dynamic Factor Model

MARÍA ELSA CORREAL1, DANIEL PEÑA2

1Universidad de los Andes, Departamento de Ingeniería Industrial, Bogotá, Colombia. Profesora asociada. Email: mcorreal@uniandes.edu.co
2Universidad Carlos III de Madrid, Departamento de Estadística y Economía, Madrid, España. Profesor catedrático. Email: dpena@est-econ.uc3m.es

Resumen

En este artículo se introduce el modelo factorial dinámico threshold, el cual permite analizar sistemas de series temporales que presenten comportamientos no lineales del tipo umbral. Se propone un método de estimación que combina el algoritmo EM con un procedimiento de búsqueda directa utilizando los algoritmos del filtro y de suavización de Kalman. El procedimiento estima factores comunes con comportamientos que cambian de régimen de acuerdo con una variable umbral.

Palabras clave: series de tiempo no lineales, análisis factorial, modelo threshold, algoritmo EM, filtro de Kalman.

Abstract

This paper introduces a threshold dynamic factor model for the analysis of vector time series which shows non-linear behavior of threshold type. We propose an estimation procedure combining an EM algorithm with a grid search procedure by the ways of the Kalman filter and smoothing recursions. We estimate common latent threshold factors that may explain the dynamic relationships within the group of variables.

Key words: Nonlinear time series, Factor analysis, Threshold model, EM algorithm, Kalman filter.

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Referencias

1. Correal, M. E. (2007), Modelo factorial dinámico con efectos umbral, Tesis doctoral, Departamento de Estadística, Facultad de Ciencias, Universidad Nacional de Colombia.

2. Forni, M., Hallin, M., Lippi, M. & Reichlin, L. (2005), `The Generalized Dynamic Factor Model: One-Sided Estimation and Forecasting´, Journal of the American Statistical Association 100, 830-840.

3. Gonzalo, J. & Pitarakis, J. Y. (2002), `Estimation and Model Selection Based Inference in Single and Multiple Threshold Models´, Journal of Econometrics 110, 319-352.

4. Hansen, B. E. (1997), `Inference in TAR Models´, Studies in Nonlinear Dynamics and Econometrics 2, 1-14.

5. Hansen, B. E. (2000), `Sample Splitting and Threshold Estimation´, Econometrica 68, 575-603.

6. Hu, Y. P. & Chou, R. J. (2004), `On the Peña-Box Model´, Journal of Time Series Analysis 25, 811-830.

7. Peña, D. & Box, G. E. P. (1987), `Identifying a Simplifying Structure in Time Series´, Journal of the American Statistical Association 82, 836-843.

8. Peña, D. & Poncela, P. (2004), `Forecasting with Nonstationary Dynamic Factor Models´, Journal of Econometrics 119, 291-321.

9. Peña, D. & Poncela, P. (2006), `Nonstationary Dynamic Factor Models´, Journal of Statistical Planning and Inference 136, 1237-1257.

10. Shumway, R. H. & Stoffer, D. S. (1982), `An Approach to Time Series Smoothing and Forecasting Using the EM Algorithm´, Journal of Time Series Analysis 3, 253-264.

11. Stock, J. H. & Watson, M. W. (2002), `Forecasting Using Principal Components From a Large Number of Predictors´, Journal of the American Statistical Association 97, 1167-1179.

12. Tsay, R. S. (1989), `Outliers, Level Shifts and Variance Changes in Time Series´, Journal of Forecasting 7, 1-20.

13. Tsay, R. S. (1998), `Testing and Modeling Multivariate Threshold Models´, Journal of the American Statistical Association 93, 1188-1202.

14. Watson, M. W. & Engle, R. F. (1983), `Alternative Algorithms for the Estimation of Dynamic Factor, Mimic and Varying Coefficient Regression Models´, Journal of Econometrics 23, 385-400.

15. Wu, L. S., Pai, J. S. & Hosking, J. R. M. (1996), `An Algorithm for Estimating Parameters of State-Space Models´, Statistics & Probability Letters 28, 99-106.

[Recibido en marzo de 2008. Aceptado en septiembre de 2008]

Este artículo se puede citar en LaTeX utilizando la siguiente referencia bibliográfica de BibTeX:

@ARTICLE{RCEv31n2a04,
    AUTHOR  = {Correal, María Elsa and Peña, Daniel},
    TITLE   = {{Modelo factorial dinámico threshold}},
    JOURNAL = {Revista Colombiana de Estadística},
    YEAR    = {2008},
    volume  = {31},
    number  = {2},
    pages   = {183-192}
}

How to Cite

APA

Correal, M. E. and Peña, D. (2008). MODELO FACTORIAL DINÁMICO THRESHOLD. Revista Colombiana de Estadística, 31(2), 183–192. https://revistas.unal.edu.co/index.php/estad/article/view/29618

ACM

[1]
Correal, M.E. and Peña, D. 2008. MODELO FACTORIAL DINÁMICO THRESHOLD. Revista Colombiana de Estadística. 31, 2 (Jul. 2008), 183–192.

ACS

(1)
Correal, M. E.; Peña, D. MODELO FACTORIAL DINÁMICO THRESHOLD. Rev. colomb. estad. 2008, 31, 183-192.

ABNT

CORREAL, M. E.; PEÑA, D. MODELO FACTORIAL DINÁMICO THRESHOLD. Revista Colombiana de Estadística, [S. l.], v. 31, n. 2, p. 183–192, 2008. Disponível em: https://revistas.unal.edu.co/index.php/estad/article/view/29618. Acesso em: 1 feb. 2025.

Chicago

Correal, María Elsa, and Daniel Peña. 2008. “MODELO FACTORIAL DINÁMICO THRESHOLD”. Revista Colombiana De Estadística 31 (2):183-92. https://revistas.unal.edu.co/index.php/estad/article/view/29618.

Harvard

Correal, M. E. and Peña, D. (2008) “MODELO FACTORIAL DINÁMICO THRESHOLD”, Revista Colombiana de Estadística, 31(2), pp. 183–192. Available at: https://revistas.unal.edu.co/index.php/estad/article/view/29618 (Accessed: 1 February 2025).

IEEE

[1]
M. E. Correal and D. Peña, “MODELO FACTORIAL DINÁMICO THRESHOLD”, Rev. colomb. estad., vol. 31, no. 2, pp. 183–192, Jul. 2008.

MLA

Correal, M. E., and D. Peña. “MODELO FACTORIAL DINÁMICO THRESHOLD”. Revista Colombiana de Estadística, vol. 31, no. 2, July 2008, pp. 183-92, https://revistas.unal.edu.co/index.php/estad/article/view/29618.

Turabian

Correal, María Elsa, and Daniel Peña. “MODELO FACTORIAL DINÁMICO THRESHOLD”. Revista Colombiana de Estadística 31, no. 2 (July 1, 2008): 183–192. Accessed February 1, 2025. https://revistas.unal.edu.co/index.php/estad/article/view/29618.

Vancouver

1.
Correal ME, Peña D. MODELO FACTORIAL DINÁMICO THRESHOLD. Rev. colomb. estad. [Internet]. 2008 Jul. 1 [cited 2025 Feb. 1];31(2):183-92. Available from: https://revistas.unal.edu.co/index.php/estad/article/view/29618

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