eval_tvRRR: Filtering for the tvRRR model

In b-brune/tvRRR: Time-varying reduced-rank regression using state-space models

Description

Run the Kalman filter for a fixed set of parameters and prespecified model A or B as defined in Brune, Bura and Scherrer (2021+).

Usage

eval_tvRRR(
  X,
  y,
  u = NULL,
  d,
  model = "A",
  alpha,
  beta,
  Gamma = NULL,
  Omega,
  Sigma,
  P_00
)

filter_modelA(
  y,
  X,
  u = NULL,
  beta,
  alpha_00,
  Gamma = NULL,
  P_00,
  Sigma,
  Omega,
  d,
  return_covariances = TRUE
)

filter_modelB(
  X,
  y,
  u = NULL,
  P_00,
  Sigma,
  Omega,
  beta_00,
  alpha,
  Gamma = NULL,
  d,
  return_covariances = TRUE
)

Arguments

X	the predictors (t x q matrix)
y	the target variable (t x p matrix)
u	(optional) additional predictors that do not necessarily vary in time (t x k matrix)
d	latent dimension (min. 1, no default)
model	specifies the model to be fitted, either "A" or "B"
alpha	starting value for the algorithm, or the time-constant parameter matrix (p x d), for model A this corresponds to alpha_00, for model B it corresponds to the time-constant parameter alpha
beta	starting value for the algorithm, or time-constant parameter matrix (q x d), for model A this corresponds to the time-constant parameter beta, for model B it corresponds to the initial state beta_00
Gamma	(optional), the time constant full rank (t x k) matrix
Omega	error covariance in the measurement equation (symmetric p x p matrix)
Sigma	column covariance of the states alpha_t (symmetric d x d matrix)
P_00	starting covariance for the algorithm (pd x pd matrix)
alpha_00	initial state
return_covariances	logical, indicates whether the filtered and smoothed covariances should be returned, defaults to FALSE.
beta_00	initial state

Details

eval_tvRRR() calls filter_modelA() or filter_modelB() respectively. filter_modelB() processes the transposed states, i.e. when directly using this function make sure you hand over the transposed matrix to beta_00.

Value

An object of class tvRRR, that is a named list of lists with elements

states

the filtered states, a named list with elements

• filtered (the filtered states) – one state matrix per row (t + 1 x p * d)

• smoothed (the smoothed states) – one state matrix per row (t + 1 x p * d)

• one-step-ahead (one-step ahead predictions of the states – one state matrix per row (t + 1 x p * d))

covariances

the filtered and smoothed covariances and lag-1 covariances, if return_covariances = TRUE, a named list with elements

• P_t^t filtered covariances – array of dimensions (t+1, pd, pd)

• P_t^t-1predicted covariances – (t, pd, pd)

• P_t^T smoothed covariances – (t+1, pd, pd)

• P_t-1t-2^T smoothed lag-1 covariances – (t, pd, pd),

else NULL

prediction_covariance

contains P_t^T[t+1, , ] which is necessary for one-step ahead prediction of tvRRR object.

data

the data handed over to the algorithms, a named list with elements

• X predictors – (t, q)

• y responses – (t, p)

• u additional predictors – (t, k)

• Z transition matrices (X_t'beta (x) I_p) – (t, p, p*d)

parameters

the parameters used for filtering:

• Sigma – (d, d)

• Omega – (p, p)

• beta – (q, d) (for model A)

• alpha – (p, d) (for model B)

b-brune/tvRRR documentation built on Dec. 19, 2021, 6:37 a.m.