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Seasonality with trend and cycle interactions in unobserved components models
Author(s) -
Koopman Siem Jan,
Lee Kai Ming
Publication year - 2009
Publication title -
journal of the royal statistical society: series c (applied statistics)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.205
H-Index - 72
eISSN - 1467-9876
pISSN - 0035-9254
DOI - 10.1111/j.1467-9876.2009.00661.x
Subject(s) - kalman filter , econometrics , series (stratigraphy) , linear model , seasonality , component (thermodynamics) , state space representation , seasonal adjustment , transformation (genetics) , logarithm , state space , time series , additive model , mathematics , computer science , statistics , algorithm , paleontology , mathematical analysis , biochemistry , physics , chemistry , variable (mathematics) , gene , biology , thermodynamics
Summary. Unobserved components time series models decompose a time series into a trend, a season, a cycle, an irregular disturbance and possibly other components. These models have been successfully applied to many economic time series. The standard assumption of a linear model, which is often appropriate after a logarithmic transformation of the data, facilitates estimation, testing, forecasting and interpretation. However, in some settings the linear–additive framework may be too restrictive. We formulate a non‐linear unobserved components time series model which allows interactions between the trend–cycle component and the seasonal component. The resulting model is cast into a non‐linear state space form and estimated by the extended Kalman filter, adapted for models with diffuse initial conditions. We apply our model to UK travel data and US unemployment and production series, and show that it can capture increasing seasonal variation and cycle‐dependent seasonal fluctuations.