Skip to main content

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 \(\lambda\)