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Prediction with incomplete past of a stationary process

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  • Bondon, Pascal

Abstract

An explicit formula is obtained for the prediction error of a future value of a stationary process when the infinite past is altered by some missing observations with an arbitrary pattern. Then the autoregressive representation of the predictor is derived and the processes for which the missing observations in the past do not affect the prediction of a future value are characterized. Some properties for autoregressive processes and for moving average processes with finite orders are established.

Suggested Citation

  • Bondon, Pascal, 2002. "Prediction with incomplete past of a stationary process," Stochastic Processes and their Applications, Elsevier, vol. 98(1), pages 67-76, March.
    • Handle: RePEc:eee:spapps:v:98:y:2002:i:1:p:67-76
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    References listed on IDEAS

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    1. Cheng, R. & Pourahmadi, M., 1997. "Prediction with incomplete past and interpolation of missing values," Statistics & Probability Letters, Elsevier, vol. 33(4), pages 341-346, May.
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    Cited by:

    1. Kasahara, Yukio & Pourahmadi, Mohsen & Inoue, Akihiko, 2009. "Duals of random vectors and processes with applications to prediction problems with missing values," Statistics & Probability Letters, Elsevier, vol. 79(14), pages 1637-1646, July.
    2. Cheng, Raymond, 2015. "Prediction of stationary Gaussian random fields with incomplete quarterplane past," Journal of Multivariate Analysis, Elsevier, vol. 139(C), pages 245-258.
    3. Kohli, P. & Pourahmadi, M., 2014. "Some prediction problems for stationary random fields with quarter-plane past," Journal of Multivariate Analysis, Elsevier, vol. 127(C), pages 112-125.

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