simulated_tci: Simulate Trend-Cycle Component

In AQLT/AQLThesis: Toolkit Functions Around AQLT Thesis

Simulate Trend-Cycle Component

Description

Simulate Trend-Cycle Component

Usage

simulated_tci(t, rho, lambda, sigma_nu, sigma_e, start = 0)

simulated_cycle(t, rho, lambda)

simulated_trend(n = 1, sigma_nu = 1, start = 0)

simulated_irregular(n = 1, sigma_e = 1)

Arguments

t, rho, lambda, sigma_nu, sigma_e, start, n

parameters, see details.

Details

The following formula is used for the cycle

C_t = \rho \[ \cos (2 \pi t / \lambda) + \sin (2 \pi t / \lambda) \]

The trend component is assumed to be a random walk with drift:

T_t = T_{t-1} + \nu_t\quad \nu_t \sim \mathcal{N}(0, \sigma_\nu^2)

The irregular component is white noise with mean zero and variance \sigma_e^2:

I_t = e_t\text{ with } e_t \sim \mathcal{N}(0, \sigma_e^2)

AQLT/AQLThesis documentation built on Feb. 7, 2024, 7:22 p.m.