SISstep.fading: Sequential Importance Sampling Step for Fading Channels
In ConvFuncTimeSeries/test_t: Nonlinear time series analysis

Description Usage Arguments Value References Examples

This function implements one step of the sequential importance sampling method for fading channels.

1	SISstep.fading(mm, xx, logww, yyy, par, xdim2, ydim)

`mm`	the Monte Carlo sample size `m`.
`xx`	the sample in the last iteration.
`logww`	the log weight in the last iteration.
`yyy`	the observations with `T` columns and `ydim` rows.
`par`	a list of parameter values. `HH` is the state coefficient model, `WWt(WW)` is the state innovation covariance matrix, `VVt(VV)` is the covariance of the observation noise, `GG` is the observation model.
`xdim2`	the dimension of the state varible `x_t`.
`ydim`	the dimension of the observation `y_t`.

The function returns a list with the following components:

`xx`	the new sample.
`logww`	the log weights.

Tsay, R. and Chen, R. (2019). Nonlinear Time Series Analysis. Wiley, New Jersey.

HH <- matrix(c(2.37409, -1.92936, 0.53028,0,1,0,0,0,0,1,0,0,0,0,1,0),ncol=4,byrow=TRUE)
WW <- matrix(c(1,0,0,0),nrow=4)
GG <- matrix(0.01*c(0.89409,2.68227,2.68227,0.89409),nrow=1)
nobs <- 10050
tt <- 50:(nobs-1)
mm <- 100; resample.sch <- rep(1,nobs)
VV <- 1.3**15*0.001
par <- list(HH=HH,WW=WW,GG=GG,VV=VV)
simu <- simu_fading(nobs,par)
ydim <- 1
mm.all <- c(100,200,500,1000,4000,8000)
kk <- 6
xdim2 <- 6
BER.S <- 1:kk
for (i in 1:kk){
	mm <- mm.all[i]
	SS0 <- diag(c(1,1,1,1))
	for(n0 in 1:20){
		SS0 <- HH%*%SS0%*%t(HH)+WW%*%t(WW)	
	}
	xx.init <- matrix(nrow=xdim2,ncol=mm)
	xx.init[1:4,] <- sqrt(SS0)%*%matrix(rnorm(4*mm),nrow=4,ncol=mm)
	xx.init[5,] <- sample.int(2,mm,0.5)
	xx.init[6,] <- rep(1,mm)
	print(c(i));flush.console()
	out <- SMC(SISstep.fading,nobs,simu$yy,mm,par,xx.init,
		xdim2,ydim,resample.sch)
	Strue <- simu$ss[2:nobs]*simu$ss[1:(nobs-1)]
	Shat <- rep(-1,(nobs-1))
	Shat[out$xhat[6,2:nobs,1]>0.5] <- 1
	BER.S[i] <- sum(abs(Strue[tt]-Shat[tt]))/(nobs-50)/2
}