Trend-Cycle VARs and DFMs
The idea of trend-cycle modeling is simple, quite old, and surprisingly underutilized in empirical econometrics and economic modeling.
In 2016, Jan Bruha and I have illustrated some in "Forecasting with Trend-Cycle VARs" [pdf] and presented the paper at the ECB, IMF, and a few conferences. In 2014, we have put forth a few key principles to adhere to when estimating and specifying VARs and Structural VARs, that also entail explicit distinction between the trends & cycles: "VAR Inferno" [pdf]
The simple idea is that a time series \(\{Y_t\} \) can be decomposed into its slow-moving (trend, low-frequency), cyclical, and noise (high-frequency) components: \[Y_t = \bar{Y_t} + \widehat{Y}_{t} + \varepsilon_t^Y. \]
The trend-cycle decomposition is quite common for DSGE models and semi-structural "gap" models, mostly associated with the IMF RES team that used to be led by Doug Laxton (see e.g. the GPM6 -- Global Projection Model of the IMF). For DSGE models, Fabio Canova illustrated that a cyclical DSGE model can be easily linked to a flexible trend specification in "Bridging DSGE Models and Raw Data."
Our approach in "Forecasting with Trend-Cycle [B]VARs" is a natural extension of the trend-cycle modeling ideas. Instead of a structural cyclical model, like a QPM/GPM, we specify a VAR or a Dynamic Factor Model (DFM), and link it to a carefully specified model of trends of each observed variable. The devil is in the detail and mistakes in the trend specifications are consequential. The trend and cyclical components need not to be independent, and a careful frequency-domain analysis of the resulting model helps to test the specification and shield the model from misspecification.
In 2016, Jan Bruha and I have illustrated some in "Forecasting with Trend-Cycle VARs" [pdf] and presented the paper at the ECB, IMF, and a few conferences. In 2014, we have put forth a few key principles to adhere to when estimating and specifying VARs and Structural VARs, that also entail explicit distinction between the trends & cycles: "VAR Inferno" [pdf]
The simple idea is that a time series \(\{Y_t\} \) can be decomposed into its slow-moving (trend, low-frequency), cyclical, and noise (high-frequency) components: \[Y_t = \bar{Y_t} + \widehat{Y}_{t} + \varepsilon_t^Y. \]
The trend-cycle decomposition is quite common for DSGE models and semi-structural "gap" models, mostly associated with the IMF RES team that used to be led by Doug Laxton (see e.g. the GPM6 -- Global Projection Model of the IMF). For DSGE models, Fabio Canova illustrated that a cyclical DSGE model can be easily linked to a flexible trend specification in "Bridging DSGE Models and Raw Data."
Our approach in "Forecasting with Trend-Cycle [B]VARs" is a natural extension of the trend-cycle modeling ideas. Instead of a structural cyclical model, like a QPM/GPM, we specify a VAR or a Dynamic Factor Model (DFM), and link it to a carefully specified model of trends of each observed variable. The devil is in the detail and mistakes in the trend specifications are consequential. The trend and cyclical components need not to be independent, and a careful frequency-domain analysis of the resulting model helps to test the specification and shield the model from misspecification.
