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Initializing The Kalman Filter For Nonstationary Time Series Models

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  • William Bell
  • Steven Hillmer

Abstract

. The problem of initializing the Kalman filter for nonstationary time series models is considered. Ansley and Kohn have developed a ‘modified Kalman filter’ for use with nonstationary models to produce estimates from what they call a ‘transformation approach’. We show that the same results can be obtained with a suitable initialization of the ordinary Kalman filter. Assuming there are d starting values for the nonstationary series, we initialize the Kalman filter using data through time d with the transformation approach estimate of the state vector and its associated error covariance matrix at time d. We give details of the initialization for ARIMA models, ARIMA component models and dynamic linear models. We present an example to illustrate how the results may differ from results obtained under more naive initializations that have been suggested.

Suggested Citation

  • William Bell & Steven Hillmer, 1991. "Initializing The Kalman Filter For Nonstationary Time Series Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 12(4), pages 283-300, July.
    • Handle: RePEc:bla:jtsera:v:12:y:1991:i:4:p:283-300
    DOI: 10.1111/j.1467-9892.1991.tb00084.x
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    Cited by:

    1. Siem Jan Koopman & John A. D. Aston, 2006. "A non-Gaussian generalization of the Airline model for robust seasonal adjustment," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 25(5), pages 325-349.
    2. McElroy Tucker S. & Maravall Agustin, 2014. "Optimal Signal Extraction with Correlated Components," Journal of Time Series Econometrics, De Gruyter, vol. 6(2), pages 1-37, July.
    3. Victor Gomez & Jorg Breitung, 1999. "The Beveridge–Nelson Decomposition: A Different Perspective with New Results," Journal of Time Series Analysis, Wiley Blackwell, vol. 20(5), pages 527-535, September.
    4. Bušs, Ginters, 2009. "Comparing forecasts of Latvia's GDP using simple seasonal ARIMA models and direct versus indirect approach," MPRA Paper 16684, University Library of Munich, Germany.
    5. Gómez, Víctor & Maravall, Agustín & Peña, Daniel, 1993. "Computing missing values in time series," DES - Working Papers. Statistics and Econometrics. WS 3737, Universidad Carlos III de Madrid. Departamento de Estadística.
    6. Idrisov, Georgy (Идрисов, Георгий) & Ponomarev, Yury (Пономарев, Юрий) & Pleskachev, Yury Andreevich (Плескачев, Юрий Андреевич), 2016. "Analysis of Joint Exchange Rate Pass-Through and Import Duty Rates in the Russian Economy [Анализ Совместного Эффекта Переноса Обменного Курса И Ввозных Пошлин В Цены В Российской Экономике]," Working Papers 1666, Russian Presidential Academy of National Economy and Public Administration.
    7. repec:jss:jstsof:41:i07 is not listed on IDEAS
    8. Maravall, Agustín & Peña, Daniel, 1992. "Missing observations and additive outliers in time series models," UC3M Working papers. Economics 2888, Universidad Carlos III de Madrid. Departamento de Economía.
    9. Alberto Cabrero & Gonzalo Camba-Mendez & Astrid Hirsch & Fernando Nieto, 2009. "Modelling the daily banknotes in circulation in the context of the liquidity management of the European Central Bank," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 28(3), pages 194-217.
    10. Regina Kaiser & Agustín Maravall, 2000. "Notes on Time Series Analysis, ARIMA Models and Signal Extraction," Working Papers 0012, Banco de España.
    11. Kaiser Remiro, Regina & Maravall, Agustín, 2000. "Notes on time serie analysis, ARIMA models and signal extraction," DES - Working Papers. Statistics and Econometrics. WS 10058, Universidad Carlos III de Madrid. Departamento de Estadística.
    12. Tucker McElroy & Thomas Trimbur, 2015. "Signal Extraction for Non-Stationary Multivariate Time Series with Illustrations for Trend Inflation," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(2), pages 209-227, March.
    13. Bernardí Cabrer Borrás & David Iranzo Pérez, 2007. "El Efecto De Los Atentados Del 11-s Sobre El Turismo En España," Estudios de Economia Aplicada, Estudios de Economia Aplicada, vol. 25, pages 365-386, Abril.
    14. S. J. Koopman & J. Durbin, 2003. "Filtering and smoothing of state vector for diffuse state‐space models," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(1), pages 85-98, January.
    15. José Casals & Sonia Sotoca & Miguel Jerez, 2012. "Minimally Conditioned Likelihood for a Nonstationary State Space Model," Documentos de Trabajo del ICAE 2012-04, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.

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