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Aggregation and Disaggregation of Structural Time Series Models
Author(s) -
Hotta Luiz K.,
Vasconcellos Klaus L.
Publication year - 1999
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/1467-9892.00131
Subject(s) - autoregressive integrated moving average , outlier , series (stratigraphy) , econometrics , autoregressive model , robustness (evolution) , time series , kalman filter , mathematics , star model , autoregressive–moving average model , aggregate (composite) , statistics , paleontology , biochemistry , chemistry , materials science , gene , composite material , biology
The aggregation/disaggregation problem has been widely studied in the time series literature. Some main issues related to this problem are modelling, prediction and robustness to outliers. In this paper we look at the modelling problem with particular interest in the local level and local trend structural time series models together with their corresponding ARIMA(0, 1, 1) and ARIMA(0, 2, 2) representations. Given an observed time series that can be expressed by a structural or autoregressive integrated moving‐average (ARIMA) model, we derive the necessary and sufficient conditions under which the aggregate and/or disaggregate series can be expressed by the same class of model. Harvey's cycle and seasonal components models (Harvey, Forecasting, Structural Time Series Models and the Kalman Filter , Cambridge: Cambridge University Press, 1989) are also briefly discussed. Systematic sampling of structural and ARIMA models is also discussed.