7 thoughts on “How to remove the trend from economic variables

  1. Tom

    I agree that the prediction object you estimate is well-defined, but in the context of trend/cycle decomposition the “cycle” component would likely be common to many economic variables (such as the national income accounts in your examples). You cite den Haan (2000) which uses a VAR prediction-error setup. Any thoughts on a multivariate extension? Would you just have the “filtered” trend data (i.e. fitted data from 4-lag regression) or cycle (residuals) in a 2nd stage VAR? In the national accounts example, the cycle should be similar which suggests a constraint on the cycle not present in a naive 2-stage regression (which suggests an iterative method).

    1. James_Hamilton Post author

      Tom: If the common trend is there my approach can find it, but if it’s not, my approach does not impose it. There’s always a trade-off: as you try to add more complexity, you lose some of the robustness. Here are my thoughts in the paper about this:

      One might be tempted to use a richer model to forecast, such as using a vector of variables, more than 4 lags, or even a nonlinear relation. However, such refinements are completely unnecessary for the goal of extracting a stationary component, and have the significant drawback that the more parameters we try to estimate by regression, the more the small-sample results are likely to differ from the asymptotic predictions. The simple univariate regression is estimating a population object that is well defined regardless of whether the variable is part of a large vector system with nonlinear dynamics. For this reason, just as the HP filter is always implemented as a univariate procedure, my recommendation is to follow that same strategy for the approach here.

      1. Tom

        Thank you, I missed that on my quick initial read. That is reasonable from a classical and exploratory perspective. However, in the spirit of your 2015 Econometrica paper with Christiane Baumeister, a multi-level model with a prior on the volatility around a common trend estimated according to your prediction specification could possibly explore the richer vector system without a multitude of parameters or imposing strong assumptions.

  2. AS

    Professor Hamilton,
    Any chance you would provide a bit more detail so those at the back of the class, who are neither economists nor mathematicians could try your process at home? I am not clear on how to use the process to make forecasts.

  3. Tanmay Satpathy

    The L1 trend filter by Kim et al , and Empirical Mode Decomposition also look like an underused alternative in economics.

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