dse (version 2006.1-1)

TSrestrictedModel: Restrict Model Coefficients

Description

Put restrictions on a "TSmodel".

Usage

TSrestrictedModel(model,
                    coefficients=NULL,
                    restriction=NULL)

Arguments

model

An object containing an object of class TSmodel (unrestricted).

coefficients

coefficients of the restricted model.

restriction

function that maps the coefficients of the restricted model into the coefficients of the unrestricted model.

concept

DSE

Details

BEWARE THIS CLASS OF MODELS IS EXPERIMENTAL AND MAY CHANGE.

This is the constructor for a "TSrestrictedModel","TSmodel""

The argument model should specify a TSmodel which is not a TSrestrictedModel.

This constructor defines a new class of model TSrestrictedModel, which is composed of an unrestricted TSmodel, a new set of coefficients, and a function called restriction which maps the new set of coefficients into the unrestricted TSmodel. So, if mod1 is a TSrestrictedModel, then mod1$restriction(mod1$TSmodel, mod1$coefficients) should return an unrestricted TSmodel with it coefficients specified. Methods like l.TSrestrictedModel sets the arrays using the set of coefficients for the TSrestrictedModel and restrictions/equalities defined in the function restriction. It is possible the class is misnamed. It should be possible to construct some extentions of TSmodels by definining restrictions on an enlarged model (but I have not played with this yet).

See Also

TSmodel, ARMA, SS, TSestModel, TSdata

Examples

rngValue10 <- list(seed=10, kind="Mersenne-Twister", normal.kind="Inversion")


#  example  1                                                                             

z <- ARMA(A=c(1, 0.3), B=1)
mod1 <- TSrestrictedModel(z, 
            coefficients=coef(z),
            restriction=function(m, AllCoef){setArrays(m, 2*AllCoef)})
mod1

#  example 2

mod2 <- TSrestrictedModel(z, coefficients=c(3, coef(z)),
       restriction=function(m, AllCoef){ setArrays(m, AllCoef[1]*AllCoef[-1])})
mod2

#  example 3

z <- toSS(ARMA(A=c(1, 0.3, 0.1), B=1))
mod3 <- TSrestrictedModel(z, coefficients=c(2,.3, 4, coef(z)),
       restriction=function(m, AllCoef){
		      mm <- setArrays(m, AllCoef[-(1:3)])
		      P0 <- matrix(0,2,2)
		      P0[,1] <- AllCoef[1:2]
		      P0[,2] <- AllCoef[2:3]
		      mm$P0 <- P0
		      setTSmodelParameters(mm)
		      })
mod3

#  example 4

#  Starting P0  ("big k") symmetric with off diagonal element smaller than diag.
P0 <- matrix(1e6,4,4) 
diag(P0 )<- 1e7

# lower triangle will be parameters
P0[outer(1:4, 1:4, ">=")]
length(P0[outer(1:4, 1:4, ">=")])  # number of parameters

Hloadings <- t(matrix(c(
    8.8,   5.2,
   23.8, -12.6,
    5.2,  -2.0,
   36.8,  16.9,
   -2.8,  31.0,
    2.6,  47.6), 2,6))

z <-  SS(F=t(matrix(c(
    		  0.8, 0.04,  0.2, 0,
    		  0.2,  0.5,    0, -0.3,
    		    1,    0,    0, -0.2,
    		    0,	  1,    0,  0   ), c(4,4))),
	       H=cbind(Hloadings, matrix(0,6,2)),	
	       Q=diag(c(1, 1, 0, 0),4),  
	       R=diag(1,6),
	       z0=c(10, 20, 30,40),
	       P0=NULL
	       )

# The restriction constructions P0 from the lower triangle 

mod4 <- TSrestrictedModel(z, 
       coefficients=c(P0[outer(1:4, 1:4, ">=")],coef(z)),
       restriction=function(m, AllCoef){
		      mm <- setArrays(m, AllCoef[-(1:10)]) 
		      P0 <- matrix(0,4,4)
		      P0[outer(1:4, 1:4, ">=")] <- AllCoef[1:10]
		      P0 <- P0 + t(P0)
		      diag(P0) <- diag(P0)/2
		      mm$P0 <- P0
		      setTSmodelParameters(mm)
		      })
mod4


z  <- simulate(SS(F=t(matrix(c(
    		  0.8, 0.04,  0.2, 0,
    		  0.2,  0.5,    0, -0.3,
    		    1,    0,    0, -0.2,
    		    0,	  1,    0,  0   ), c(4,4))),
	       H=cbind(Hloadings, matrix(0,6,2)),	
	       Q=diag(c(1, 1, 0, 0),4),  
	       R=diag(1,6),
	       z0=c(10, 20, 30,40),
	       P0=diag(c(10, 10, 10, 10)) ),
               rng=rngValue10)  
state.sim  <- z$state  # for comparison below
y.sim  <- outputData(z) # simulated indicators

coef(mod4)
coef(l(mod4, TSdata(output=y.sim)))
summary(l(mod4, TSdata(output=y.sim))) 


zz <- smoother(l(mod4, TSdata(output=y.sim)))  
summary(zz)

tfplot(state.sim,state(zz))
tfplot(state.sim,state(zz, smoother=TRUE))

est.mod4 <- estMaxLik(mod4, TSdata(output=y.sim),
        algorithm.args=list(method="BFGS", upper=Inf, lower=-Inf, hessian=TRUE,
                        control=list(maxit=10000))
    ) 

summary(est.mod4)

sest.mod4 <- smoother(est.mod4)
summary(sest.mod4)

tfplot(sest.mod4, graphs.per.page=3)
tfplot(state.sim, state(sest.mod4, smoother=TRUE))
tfplot(state.sim, state(sest.mod4, filter=TRUE))

coef(sest.mod4)
coef(mod4)