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ARIMA model; exponential smoothing of order $m$; discounted least squares; irregular observations; maximum likelihood; simple exponential smoothing; time series
The paper deals with extensions of exponential smoothing type methods for univariate time series with irregular observations. An alternative method to Wright’s modification of simple exponential smoothing based on the corresponding ARIMA process is suggested. Exponential smoothing of order m for irregular data is derived. A similar method using a DLS **discounted least squares** estimation of polynomial trend of order m is derived as well. Maximum likelihood parameters estimation for forecasting methods in irregular time series is suggested. The suggested methods are compared with the existing ones in a simulation numerical study.
[1] Abraham B., Ledolter J.: Statistical Methods for Forecasting. Wiley, New York 1983 MR 0719535 | Zbl 1082.62079
[2] Aldrin M., Damsleth E.: Forecasting non-seasonal time series with missing observations. J. Forecasting 8 (1989), 97–116
[3] Anděl J., Zichová J.: A method for estimating parameter in nonnegative MA(1) models. Comm. Statist. Theory Methods 31 (2002), 2101–2111 MR 1946313 | Zbl 1051.62070
[4] Chatfield C.: Time-Series Forecasting. Chapman & Hall/CRC, 2002
[5] Cipra T., Trujillo, J., Rubio A.: Holt–Winters method with missing observations. Manag. Sci. 41 (1995), 174–8 Zbl 0829.90034
[6] Cipra T.: Exponential smoothing for irregular data. Appl. Math. 51 (2006), 597–604 MR 2291784 | Zbl 1164.62377
[7] Wright D. J.: Forecasting data published at irregular time intervals using extension of Holt’s method. Manag. Sci. 32 (1986), 499–510
[8] Zichová J.: On a method of estimating parameters in non-negative ARMA models. Kybernetika 32 (1996), 409–424 MR 1420132 | Zbl 0882.62089
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