Package 'wex'

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

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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)

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