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Table 3 Business-cycles duration

From: Trend-cycle decomposition for Peruvian GDP: application of an alternative method

  UC-0 UC-C UC-N UC-P UC-CN UC-CP UC-NP UC-CNP
Autoregressive parameters
\(\phi _{1}\) 1.353 1.496 1.361 1.276 1.416 1.506 1.159 1.276
\(\phi _{2}\) −0.432 −0.544 −0.676 −0.504 −0.519 −0.553 −0.878 −0.770
Roots of the inverse polynomial
\(\lambda _{1}\) 0.837 0.875 0.68 + 0.5i 0.64 + 0.3i 0.71 + 0.1i 0.873 0.58 + 0.7i 0.64 + 0.6i
\(\lambda _{2}\) 0.515 0.621 0.68 − 0.5i 0.64 − 0.3i 0.71 − 0.1i 0.634 0.58 − 0.7i 0.64 − 0.6i
Implicit duration of cycles (years)
    2.6 3.5 8.5   1.7 2.1
  1. The implicit duration of cycles is given by \(d=\frac{2\pi }{\theta}, \cos\left( \theta \right) =\frac{a}{R},\) where a and R are the real part and the module of root \(\lambda\)