A trend-cycle(-season) filter
AbstractThis paper proposes a new univariate method to decompose a time series into a trend, a cyclical and a seasonal component: the Trend-Cycle filter (TC filter) and its extension, the Trend-Cycle-Season filter (TCS filter). They can be regarded as extensions of the Hodrick-Prescott filter (HP filter). In particular, the stochastic model of the HP filter is extended by explicit models for the cyclical and the seasonal component. The introduction of a stochastic cycle improves the filter in three respects: first, trend and cyclical components are more consistent with the underlying theoretical model of the filter. Second, the end-of sample reliability of the trend estimates and the cyclical component is improved compared to the HP filter since the pro-cyclical bias in end-of-sample trend estimates is virtually removed. Finally, structural breaks in the original time series can be easily accounted for. JEL Classification: C13, C22, E32
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Bibliographic InfoPaper provided by European Central Bank in its series Working Paper Series with number 0499.
Date of creation: Jul 2005
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Other versions of this item:JEL classification:
- 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
- E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles
This paper has been announced in the following NEP Reports:
- NEP-ALL-2005-10-04 (All new papers)
- NEP-DGE-2005-10-04 (Dynamic General Equilibrium)
- NEP-ETS-2005-10-04 (Econometric Time Series)
- NEP-MAC-2005-10-04 (Macroeconomics)
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