Help for package wex

Type:

Package

Title:

Exact Observation Weights for the Kalman Filter and Smoother

Version:

0.1.1

Maintainer:

Tim Ginker <timginker@gmail.com>

Description:

Computes exact observation weights for the Kalman filter and smoother, following Koopman and Harvey (2003) <www.sciencedirect.com/science/article/pii/S0165188902000611>. The package provides tools for analyzing linear Gaussian state-space models, allowing users to quantify the contribution of individual observations to filtered and smoothed state estimates. These weights can be used for interpretation, decomposition, and diagnostic analysis in time series models, including applications such as dynamic factor models. See the README for examples.

License:

MIT + file LICENSE

Encoding:

UTF-8

Imports:

FKF, KFAS

LazyData:

true

URL:

https://github.com/timginker/wex

BugReports:

https://github.com/timginker/wex/issues

RoxygenNote:

7.3.3

NeedsCompilation:

Packaged:

2026-04-03 17:51:51 UTC; timgi

Author:

Tim Ginker

[aut, cre, cph]

Depends:

R (≥ 3.5.0)

Repository:

CRAN

Date/Publication:

2026-04-04 05:20:02 UTC

Sample Data with 10 Economic Indicators

Description

A dataset containing 10 monthly economic indicators, covering the period from January 2000 to November 2021. All variables have been log-differenced, when necessary, to achieve stationarity.

Usage

indicators

Format

A data frame with 263 rows and 11 variables:

date: Date values (format: YYYY-MM-DD)
total_production: Total industrial production in Israel
retail_revenue: Trade revenue
services_revenue: Service revenue
employment: Employment (excluding absent workers)
export_services: Exports of services
building_starts: Building starts
import_consumer_goods: Imports of consumer goods
import_production_inputs: Imports of production inputs
export_goods: Exports of goods
job_openings: Job openings

Source

Public data from various sources

Exact observation weights for the Kalman filter and smoother

Description

Computes the exact observation weights for the Kalman filter and smoother, following Koopman and Harvey (2003). The implementation in wex builds on the functionality provided by the FKF and KFAS packages. These packages rely on different computational approaches: FKF uses routines from BLAS and LAPACK, whereas KFAS uses sequential processing, which allows the prediction error variance matrices to be singular.

Usage

wex(a0 = NULL, P0 = NULL, Tt, Zt, HHt, GGt, yt, t, package = "FKF")

Arguments

a0

A numeric vector specifying the initial state estimate. Defaults to a vector of zeros.

P0

A numeric matrix specifying the covariance matrix of the initial state. Defaults to a diagonal matrix with large values (e.g., 1e6) on the diagonal.

Tt

An array specifying the transition matrix of the state equation (see Details).

Zt

An array specifying the observation matrix of the measurement equation (see Details).

HHt

An array specifying the covariance matrix of the state disturbances (see Details).

GGt

An array specifying the covariance matrix of the observation disturbances (see Details).

yt

An d \times n matrix of observations, where rows correspond to variables and columns to time points. Missing values (NA) are allowed.

t

An integer specifying the time index for which the observation weights are evaluated.

package

A character string indicating which backend to use ("FKF" or "KFAS"). Defaults to "FKF".

Details

State space form

\alpha_{t+1} = T_t \alpha_t + H_t \eta_t,

y_t = Z_t \alpha_t + G_t \epsilon_t,

where y_t represents the observed data (possibly with NA's), and \alpha_t is the state vector.

Value

A list with two components:

Wt: An array of filtering weights with dimensions m \times d \times n, , where m is the state dimension, d is the observation dimension, and n is the number of time points.
WtT: An array of smoothing weights with the same dimensions as Wt.

Author(s)

Tim Ginker

References

Koopman, S. J., and Harvey, A. (2003). Computing observation weights for signal extraction and filtering. Journal of Economic Dynamics and Control, 27(7), 1317-1333.

Helske, J. (2017). KFAS: Exponential family state space models in R. Journal of Statistical Software, 78, 1-39.

Examples


# Decompose a local level model (Nile data set)
data(Nile)
y <- Nile
wts <- wex(Tt=matrix(1),
Zt=matrix(1),
HHt = matrix(1385.066),
GGt = matrix(15124.13),
yt = t(y),
t=50)