# hmm.sim: Simulate a Gaussian hidden Markov series with / without... In rarhsmm: Regularized Autoregressive Hidden Semi Markov Model

## Description

Simulate a Gaussian hidden Markov series with / without autoregressive structures

## Usage

 `1` ```hmm.sim(ns, mod) ```

## Arguments

 `ns` length of the simulated series `mod` list consisting of at least the following items: mod\$m = number of states, mod\$delta = vector of prior probabilities, mod\$gamma = matrix of state transition probabilies. mod\$mu = list of means, mod\$sigma = list of covariance matrices. For autoregressive hidden markov models, we also need the additional items: mod\$auto = list of autocorrelation matrices. mod\$arp = order of autoregressive.

## Value

a list containing simulated series and states

## References

Rabiner, Lawrence R. "A tutorial on hidden Markov models and selected applications in speech recognition." Proceedings of the IEEE 77.2 (1989): 257-286.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29``` ```set.seed(135) #Gaussian HMM 3 hidden states (no autoregressive structure) m <- 3 mu <- list(c(3),c(-2),c(0)) sigma <- list(as.matrix(1), as.matrix(0.8),as.matrix(0.3)) delta <- c(0.3,0.3,0.4) gamma <- matrix(c(0.8,0.1,0.1,0.1,0.8,0.1,0.1,0.1,0.8),3,3,byrow=TRUE) mod1 <- list(m=m,mu=mu,sigma=sigma,delta=delta,gamma=gamma) sim1 <- hmm.sim(1000,mod1) y1 <- sim1\$series fit1 <- em.hmm(y=y1, mod=mod1) #AR(2) Gaussian HMM with 3 hidden states m <- 2 mu <- list(c(3,4,5),c(-2,-3,-4)) sigma <- list(diag(1.3,3), matrix(c(1,-0.3,0.2,-0.3,1.5,0.3,0.2,0.3,2),3,3,byrow=TRUE)) delta <- c(0.5,0.5) gamma <- matrix(c(0.8,0.2,0.1,0.9),2,2,byrow=TRUE) auto <- list(matrix(c(0.3,0.2,0.1,0.4,0.3,0.2, -0.3,-0.2,-0.1,0.3,0.2,0.1, 0,0,0,0,0,0),3,6,byrow=TRUE), matrix(c(0.2,0,0,0.4,0,0, 0,0.2,0,0,0.4,0, 0,0,0.2,0,0,0.4),3,6,byrow=TRUE)) mod2 <- list(m=m,mu=mu,sigma=sigma,delta=delta,gamma=gamma,auto=auto,arp=2) sim2 <- hmm.sim(2000,mod2) y2 <- sim2\$series fit2 <- em.hmm(y=y2, mod=mod2, arp=2) ```

### Example output

```iteration  1 ; loglik =  -1777.694
iteration  2 ; loglik =  -1772.407
iteration  3 ; loglik =  -1772.029
iteration  4 ; loglik =  -1771.931
iteration  5 ; loglik =  -1771.902
iteration  6 ; loglik =  -1771.894
iteration  7 ; loglik =  -1771.892
iteration  8 ; loglik =  -1771.891
iteration  9 ; loglik =  -1771.89
iteration  1 ; loglik =  -10181.56
iteration  2 ; loglik =  -10152.32
iteration  3 ; loglik =  -10152.32
```

rarhsmm documentation built on May 2, 2019, 9:33 a.m.