Abstract
The problem introduced in this paper originated from a water pollution study of the Menomenee River in Milwaukee, Wisconsin. The final goal of the study was to estimate the total pollutant load deposited in Lake Michigan, for a given season. However, the information on the concentration of pollutants was not complete. Concentration data were available for only 20% of the days in the study period. Complete data were available on two related series: river flow rate and water equivalent of precipitation. Those series were used along with the pollutant concentration data to create a model for pollutant behavior (for the different pollutants and years), to estimate the missing observations and to estimate total pollutant loading for several seasons. (See Miller, et al (1980).)
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References
Brubacker, S. and Wilson, G. (1976). Interpolating time series with applications to the estimation of holiday effects on electricity demand. JRSSC, 25, 107–116.
Clinger, W. and Vanness, H.W. (1976). On unequally spaced time points in time series. Annals of Statistics, 4, 736–745.
Dempster, A., Laird, N., and Rubin, D. (1977). Maximum likelihood from incomplete data via the E-M algorithm. JRSSB, 39, 1–22.
Dunsmuir, W., and Hannan, E.J. (1976). Vector linear time series models. Advances of Applied Probability, 8, 339–364.
Dunsmuir, W., and Robinson, P.M. (1979). Estimation of time series models in the presence of missing data. Technical Report No. 9, M.I.T. Statistics Group, Mathematics Department.
Dunsmuir, W., and Robinson, P.M. (1981a). Asymptotic theory for time series containing missing and amplitude modulated observations”. Sankhya, Ser. A, 43.
Dunsmuir, W., and Robinson, P.M. (1981b). Parametric estimators for stationary time series with missing observations. Advances of Applied Probability, 13, 129–146.
Jones, R.H. (1962). Spectral analysis with regularly missed observations. Annals of Mathematical Statistics, 33, 455–461.
Jones, R.H. (1980). Maximum likelihood fitting of ARMA models to time series with missing observations. Technometrics 22, 389–395.
Miller, R., Bell, W., Ferreiro, O., and Wang, Y (1980). Regional inferences based on water quality monitoring data. Water Resources Center, University of Wisconsin, Technical Report No. 80-05.
Parzen, E. (1963). “On spectral analysis with missing observations and amplitude modulation. Sankhya, Ser. A, 25, 383–392.
Robinson, P.M. (1977). Estimation of a time series model from unequally spaced data. Stochastic Processes and Their Applications, 6, 9–24.
— (1980). Continuous model fitting from discrete data. Directions in Time Series, ed. D.R. Brillinger and G.C. Tiao, Institute of Mathematical Statistics, 263-278.
Scheinok, P.S. (1965). Spectral analysis with randomly missed observations: The Binomial Case. Annals of Mathematical Statistics, 36, 971–977.
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© 1984 Springer-Verlag Berlin Heidelberg
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Miller, R.B., Ferreiro, O. (1984). A Strategy to Complete a Time Series with Missing Observations. In: Parzen, E. (eds) Time Series Analysis of Irregularly Observed Data. Lecture Notes in Statistics, vol 25. Springer, New York, NY. https://doi.org/10.1007/978-1-4684-9403-7_12
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DOI: https://doi.org/10.1007/978-1-4684-9403-7_12
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