xSVfilter = function(num, y, phi0, phi1, sQ, alpha, sR0, mu1, sR1){

# THIS IS SCHEDULED TO BE REMOVED

  #  see: http://www.stat.pitt.edu/stoffer/booty.pdf  section 2.2 for details
  #  y is log(return^2)  -  x is log-volatility 
  #  model is   x_t+1 = phi0 + phi1*x_t + w_t
  #             y_t   = alpha + x_t + v_t  
  #             v_t is a mixture,  
  #

# Initialize
 Q  = sQ^2
 R0 = sR0^2
 R1 = sR1^2
 xp = c(0) #  x_t+1^t
 Pp = c(phi1^2 + Q)    #  P_t+1^t

 pi1  = .5    # initial mix probs
 pi0  = .5
 pit1 = .5 
 pit0 = .5 
 like =  0    # -log(likelihood)
#
for (i in 2:num){
  sig1 = Pp[i-1] + R1     # innov var
  sig0 = Pp[i-1] + R0 
  k1   = phi1*Pp[i-1]/sig1
  k0   = phi1*Pp[i-1]/sig0
  e1   = y[i] - xp[i-1] - mu1 - alpha
  e0   = y[i] - xp[i-1] - alpha
  den1 = (1/sqrt(sig1))*exp(-.5*e1^2/sig1)
  den0 = (1/sqrt(sig0))*exp(-.5*e0^2/sig0)
  denom = pi1*den1 + pi0*den0
  pit1  = pi1*den1/denom
  pit0  = pi0*den0/denom
#  
  xp[i] = phi0 + phi1*xp[i-1] + pit0*k0*e0 + pit1*k1*e1
  Pp[i] = (phi1^2)*Pp[i-1] + Q - pit0*(k0^2)*sig0 - pit1*(k1^2)*sig1
#
  like = like - 0.5*log(pi1*den1 + pi0*den0)
 }
 list(xp=xp, Pp=Pp, like=like)
}

