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Missing observations and additive outliers in time series models

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  • Maravall, Agustín
  • Peña, Daniel

Abstract

The paper deals with estimation of missing observations in possible nonstationary ARIMA models. First, the model is assumed known, and the structure of the interpolation filter is analyzed. Using the inverse or dual autocorrelation function it is seen how estimation of a missing observation is analogous to the removal of an outlier effect; both problems are closely related with the signal plus noise decomposition of the series. The results are extended to cover, first, the case of a missing observation near the two extremes of the series; then to the case of a sequence of missing observations, and finally to the general case of any number of sequences of any length of missing observations. The optimal estimator can always be expressed, in a compact way, in terms of the dual autocorrelation function or a truncation thereof; is mean squared error is equal to the inverse of the (appropriately chosen) dual autocovariance matrix. The last part of the paper illustrates a point of applied interest: When the model is unknown, the additive outlier approach may provide a convenient and efficient alternative to the standard Kalman filter-fixed point smoother approach for missing observations estimation.

Suggested Citation

  • 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.
    • Handle: RePEc:cte:werepe:2888
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    References listed on IDEAS

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    1. S. R. Brubacher & G. Tunnicliffe Wilson, 1976. "Interpolating Time Series with Application to the Estimation of Holiday Effects on Electricity Demand," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 25(2), pages 107-116, June.
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    3. Arnold Zellner, 1978. "Seasonal Analysis of Economic Time Series," NBER Books, National Bureau of Economic Research, Inc, number zell78-1, March.
    4. Francesco Battaglia, 1983. "Inverse Autocovariances And A Measure Of Linear Determinism For A Stationary Process," Journal of Time Series Analysis, Wiley Blackwell, vol. 4(2), pages 79-87, March.
    5. Piet De Jong, 1991. "Stable Algorithms For The State Space Model," Journal of Time Series Analysis, Wiley Blackwell, vol. 12(2), pages 143-157, March.
    6. Maravall, Agustin, 1987. "Minimum Mean Squared Error Estimation of the Noise in Unobserved Component Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 5(1), pages 115-120, January.
    7. Nerlove, Marc & Grether, David M. & Carvalho, José L., 1979. "Analysis of Economic Time Series," Elsevier Monographs, Elsevier, edition 1, number 9780125157506 edited by Shell, Karl.
    8. 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.
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    Cited by:

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    2. Chin Wen Cheong & Ng Sew Lai & Nurul Afidah Mohmad Yusof & Khor Chia Ying, 2012. "Asymmetric Fractionally Integrated Volatility Modelling of Asian Equity Markets under the Subprime Mortgage Crisis," Journal of Quantitative Economics, The Indian Econometric Society, vol. 10(1), pages 70-84, January.
    3. Pedro Delicado & Ana Justel, 1997. "Forecasting with missing data: Application to a real case," Economics Working Papers 213, Department of Economics and Business, Universitat Pompeu Fabra.
    4. Alanya-Beltran, Willy, 2022. "Unit roots in lower-bounded series with outliers," Economic Modelling, Elsevier, vol. 115(C).
    5. Mohamed El Hedi Arouri & Jamel Jouini & Nhu Tuyen Le & Duc Khuong Nguyen, 2012. "On the Relationship between World Oil Prices and GCC Stock Markets," Journal of Quantitative Economics, The Indian Econometric Society, vol. 10(1), pages 98-120, January.
    6. Gomez, Victor & Maravall, Agustin & Pena, Daniel, 1998. "Missing observations in ARIMA models: Skipping approach versus additive outlier approach," Journal of Econometrics, Elsevier, vol. 88(2), pages 341-363, November.
    7. Delicado, Pedro, 1995. "Predicción con datos faltantes: aplicación a un caso real," DES - Documentos de Trabajo. Estadística y Econometría. DS 3583, Universidad Carlos III de Madrid. Departamento de Estadística.

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    More about this item

    Keywords

    ARIMA models;

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • 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

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