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My memory is fuzzy on the advantages and disadvantages of various methods for detrending time-series data. I'm looking for a succinct summary of why and when one should or should not use the following:

  • Differenced data
  • Log-differenced data
  • Error term, after regressing on only a linear or polynomial time series (e.g., 0,1,2,3,...,t)
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Differenced data

USE: When the series resembles that of a random walk, taking first differences makes it stationary, so that it can be described as linear series representation of autoregressive or moving average terms.

DO NOT USE: When the series appears to randomly fluctuate around its mean.

Log-differenced

USE: Similar to simple differencing but applied when the variance in the series is assumed to depend on the level. Or when the series is an index.

DO NOT USE: When there's no such assumption or where the series is not strictly positive.

Error term

In classical time series decomposition you should proceed as follows:

  1. Decide on whether taking logs of original series is reasonable

  2. Decide on whether regression on time variable is reasonable

  3. Decide on whether to take differences of the residuals

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