In the context of macroeconomic data, and since our interest is on the long-run behaviour, we first remove the business cycle component of Xit by employing the Hodrick–Prescott (1997) filter. The only input required is a smoothing parameter determined mainly by the frequency of the data.Having extracted the trend component from the series denoted asˆ
Xit, we calculate the estimated transition paths asˆ
hit=ˆ
Xit/(1/N)ˆXit. Next, we construct the cross-sectional variation ratio H1/Ht, where