kfMFPD: Kalman marginal (forward) filtering computation and...
In ilyaZar/RcppSMCkalman: Kalman Filtering and Backward Simulation via RcppSMC

View source: R/02_kf_MF.R

kfMFPD

R Documentation

Kalman marginal (forward) filtering computation and prediction

Description

Runs (Marginal) filtering and prediction recursions, as described in the corresponding "(Marginal) Filtering and prediction - implemented recursions" subsection of the Details section in kfLGSSM.

Usage

kfMFPD(
  yObs,
  uReg,
  wReg,
  dimX,
  dimY,
  TT,
  x00,
  P00,
  u00,
  A,
  B,
  C,
  D,
  Q,
  R,
  PDSTORE = FALSE
)

Arguments

`yObs`	A matrix or vector of measurements (observations): rows: multivariate dimension columns: time series dimension `T` If `Y` is a univariate process, `yObs` can be passed as a vector of length `T`. If `nrow(yObs) = 1`, then `yObs` becomes a vector of length `T`.
`uReg`	Matrix (vector) of regressors for the latent state process of dimension `ncol(B) x T`. For a single regressors `uReg` is a vector of length `T`.
`wReg`	Matrix (vector) of regressors for the measurement process of dimension `ncol(D) x T`. For a single regressors `wReg` is a vector of length `T`.
`dimX`	integer giving the dimension of the latent state process
`dimY`	integer giving the dimension of the measurement process
`TT`	integer giving the length of the time series
`x00`	see `initX` from `kfLGSSM`
`P00`	see `initP` from `kfLGSSM`
`u00`	see `initU` from `kfLGSSM`
`A`	Parameter (or system) matrix of dimension `dimX x dimX`.
`B`	Parameter (or system) matrix of dimension `dimX x numU`.
`C`	Parameter (or system) matrix of dimension `dimY x dimX`.
`D`	Parameter (or system) matrix of dimension `dimY x numW`.
`Q`	Error VCM of state process of dimension `dimX x dimX`.
`R`	Error VCM of measurement process of dimension `dimY x dimY`
`PDSTORE`	logical; if `TRUE` prediction quantities `\hat{P}_{t\|t-1}` and `\hat{x}_{t\|t-1}` are stored `\forall t=1,\ldots,T`; otherwise, only stored for current iteration `t` and not returned.

Value

if PDSTORE = FALSE a named list of two

mfdEXP a matrix of dimension dimX x TT with each column being the corresponding \hat{x}_{t|t} (see the Details section in kfLGSSM).
mfdVAR an array of dimension dimX x dimX x TT with matrices \hat{P}_{t|t} of dimension dimX x dimX \forall t = 1,\ldots,TT (see the Details section in kfLGSSM).

if PDSTORE = TRUE a named list of four:

mfdEXP as above
mfdVAR as above
pddEXP a matrix of dimension dimX x (TT + 1) with each column being the corresponding \hat{x}_{t+1|t}, starting from \hat{x}_{1|0} and running to \hat{x}_{T+1|T} (see the Details section in kfLGSSM).
pddVAR an array of dimension dimX x dimX x (TT + 1) with matrices \hat{P}_{t+1|t} of dimension dimX x dimX, \forall t = 1, \ldots,TT + 1, starting with \hat{P}_{1|0} and running to \hat{P}_{T+1|T} (see the Details section in kfLGSSM).