sigex.lpfiltering: Compute signal extraction estimates with uncertainty for...

In jlivsey/sigex: Ecce Signum: Multivariate Signal Extraction

Compute signal extraction estimates with uncertainty 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. The error spectral density calculations are found in: "Casting Vector Time Series: Algorithms for Forecasting, Imputation, and Signal Extraction," McElroy (2018). 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.lpfiltering(
  mdl,
  data.ts,
  trendcyclecomp,
  sigcomps,
  psi,
  cutoff,
  grid,
  window,
  trunc,
  trendFlag
)

Arguments

mdl	The specified sigex model, a list object
data.ts	A T x N matrix ts object
trendcyclecomp	The (single) index of the trend-cycle component
sigcomps	Provides indices of a desired component that is disjoint from trend-cycle, so that MSEs of trend+sigcomps and cycle+sigcomps are computed. (Pass in sigcomps = NULL to just get trend and cycle MSEs.)
psi	A vector of all the real hyper-parameters
cutoff	A number between 0 and pi, with all frequencies < cutoff preserved
grid	Desired number of frequencies for spectrum calculations
window	Maximum index of the filter coefficients
trunc	Truncation index for LP filter
trendFlag	Boolean flag, TRUE for trend+signal, else get cycle+signal

Details

Notes: Starts with LP an ideal low-pass filter, and applies LP*WK filter with cutoff parameter to each component, where the filter has been truncated to length 2*window + 1. The output will be LP*WK filter applied to data, which is forecast and aftcast extended by window units, covering time points 1-window ..., T+window. This gives trend and cycle at times 1,...,T. Take grid >> window, else numerical issues arise

Value

list object with lp.signal, upp, and low lp.signal: T x N matrix of the signal estimates upp: as lp.signal, plus twice the standard error low: as lp.signal, minus twice the standard error

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