X11 decomposition

Additive decomposition

Pseudo-additive decomposition

Step A

Step B

Step C

Step D

Remove extreme values

Additive

\(Y = T + S + \left( I + \tilde I \right)\) \(Y - \tilde I = T + S + I\) \(D_1 = Y - C_{20}\)

Multiplicative

\(Y = T \times S \times \left( I \times \tilde I \right)\) \(Y / \tilde I = T \times S \times I\) \(D_1 = Y / C_{20}\)

Pseudo-additive

\(Y = T \times \left(S + \left( I \times \tilde I \right)-1\right) = T \times \left(S + I-1 + \left( I \times \tilde I -I\right)\right)\) \(Y + T \times \left(I - I \times \tilde I) \right) = T \times \left( S + I - 1\right)\) \(D_1 = Y + C_7 (C_{13}/C_{20}-C_{13})\)