# MKF.Full.RB: Full Information Propagation Step under Mixture Kalman Filter In NTS: Nonlinear Time Series Analysis

 MKF.Full.RB R Documentation

## Full Information Propagation Step under Mixture Kalman Filter

### Description

This function implements the full information propagation step under mixture Kalman filter with full information proposal distribution and Rao-Blackwellization, no delay.

### Usage

``````MKF.Full.RB(
MKFstep.Full.RB,
nobs,
yy,
mm,
par,
II.init,
mu.init,
SS.init,
xdim,
ydim,
resample.sch
)
``````

### Arguments

 `MKFstep.Full.RB` a function that performs one step propagation under mixture Kalman filter, with full information proposal distribution. Its input includes `(mm,II,mu,SS,logww,yyy,par,xdim,ydim)`, where `II`, `mu`, and `SS` are the indicators and its corresponding mean and variance matrix of the Kalman filter components in the last iterations. `logww` is the log weight of the last iteration. `yyy` is the observation at current time step. It should return the Rao-Blackwellization estimation of the mean and variance. `nobs` the number of observations `T`. `yy` the observations with `T` columns and `ydim` rows. `mm` the Monte Carlo sample size `m`. `par` a list of parameter values to pass to `Sstep`. `II.init` the initial indicators. `mu.init` the initial mean. `SS.init` the initial variance. `xdim` the dimension of the state varible `x_t`. `ydim` the dimension of the observation `y_t`. `resample.sch` a binary vector of length `nobs`, reflecting the resampling schedule. resample.sch[i]= 1 indicating resample should be carried out at step `i`.

### Value

The function returns a list with components:

 `xhat` the fitted value. `xhatRB` the fitted value using Rao-Blackwellization. `Iphat` the estimated indicators. `IphatRB` the estimated indicators using Rao-Blackwellization.

### References

Tsay, R. and Chen, R. (2018). Nonlinear Time Series Analysis. John Wiley & Sons, New Jersey.

NTS documentation built on Sept. 25, 2023, 1:08 a.m.