sigex.lpwk: Computes signal extraction filter coefficients for trend and...

In jlivsey/sigex: Ecce Signum: Multivariate Signal Extraction

Computes signal extraction filter coefficients for trend and cycle, by combining WK filter for trend-cycle (specified by trendcyclecomp) with LP filter of cutoff.

Description

Background: A sigex model consists of process x = sum y, for stochastic components y. Each component process y_t is either stationary or is reduced to stationarity by application of a differencing polynomial delta(B), i.e. w_t = delta(B) y_t is stationary. We have a model for each w_t process, and can compute its autocovariance function (acf), and denote its autocovariance generating function (acgf) via gamma_w (B). The signal extraction filter for y_t is determined from this acgf and delta. param is the name for the model parameters entered into a list object with a more intuitive structure, whereas psi refers to a vector of real numbers containing all hyper-parameters (i.e., reals mapped bijectively to the parameter manifold)

Usage

sigex.lpwk(data.ts, param, mdl, trendcyclecomp, grid, len, cutoff, trunc)

Arguments

data.ts	A T x N matrix ts object
param	model parameters entered into a list object with an intuitive structure.
mdl	The specified sigex model, a list object
trendcyclecomp	The (single) index of the trend-cycle component
grid	Desired number of frequencies for spectrum calculations
len	Max index of the filter coefficients
cutoff	A number between 0 and pi, with all frequencies < cutoff preserved
trunc	Truncation index for LP filter

Details

Notes: take grid >> len, else numerical issues arise

Value

list object with psi.lpwk and psi.ilpwk psi.lpwk: array of dimension c(N,N,2*trunc+1), filter coefficients for trend psi.ilpwk: array of dimension c(N,N,2*trunc+1), filter coefficients for cycle

jlivsey/sigex documentation built on March 20, 2024, 3:17 a.m.