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The estimation of dynamic models with missing observations

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  • Harvey, A. C.
  • Pereira, Pedro Luiz Valls

Abstract

An ARMA model can be put in state space form and its exact likelihood function calculated by the Kalman filter. The same technique can be extended to handle missing observations, including cases where the data are initially available at an annual level and subsequently become available on a quartely, or monthly, basis. The Kalman filter enables the likelihood function to be computed for both stock and flow data. Once a suitable model has been fitted, the missing observations may be estimated by "smoothing". The paper first sets out the Kalman filter approach to missing observations for an ARMA time series model and discusses the implementation of an efficient algorithm. The results are then extended to cover static regression models with ARMA disturbances and dynamic models. A series of Monte Carlo experiments comparing the efficiency of different estimation procedures are reported.

Suggested Citation

  • Harvey, A. C. & Pereira, Pedro Luiz Valls, 1985. "The estimation of dynamic models with missing observations," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 5(2), November.
    • Handle: RePEc:sbe:breart:v:5:y:1985:i:2:a:3126
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    References listed on IDEAS

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    1. G. Gardner & A. C. Harvey & G. D. A. Phillips, 1980. "An Algorithm for Exact Maximum Likelihood Estimation of Autoregressive–Moving Average Models by Means of Kaiman Filtering," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 29(3), pages 311-322, November.
    2. Sargan, J D & Drettakis, E G, 1974. "Missing Data in an Autoregressive Model," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 15(1), pages 39-58, February.
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    Cited by:

    1. Ito, Nobuyasu, 1993. "Non-equilibrium relaxation and interface energy of the Ising model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 196(4), pages 591-614.

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