ABSTRACT
Using non-Gaussian state-space models, Perron and Wada (2009, Journal of Monetary Economics, 56, 749–765) obtained a nearly piecewise linear trend estimate of US real gross domestic product such that its slope changed around 1973. Such a trend may be regarded as a result of occasional permanent shocks to the growth rate. This article shows that the trend filtering, which is quite similar to the Hodrick–Prescott filtering and is a type of the recently popular lasso regression, yields almost the same trend estimate, and discusses the reason why this occurs.
Disclosure statement
No potential conflict of interest was reported by the author.
Notes
1 See also Tibshirani and Taylor (Citation2011) and Tibshirani (Citation2014).
2 For further explanations, see Yamada and Jin (Citation2013) and Yamada and Yoon (Citation2014, Citation2016).
3 See, e.g., Tibshirani (Citation1996).
4 We set in Equation 1 because Perron and Wada (Citation2009) note that the results from the HP filtering with
are basically equivalent to their trend-cycle decomposition with a trend that has a single shift in slope in 1973.
5 We thank Professors Perron and Wada for providing their data set and Matlab codes. The Matlab codes were used to produce .
6 See Figure 7 of Tibshirani (Citation1996).