LOCALDLM Procedure

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@LOCALDLM sets up the matrices for a local level or local trend state space model.

@LOCALDLM( options ) (no parameters)

Options

TYPE=[LEVEL]/TREND

A=(output) the state transition matrix

C=(output) the coefficient matrix

F=(output) the loadings from the state shocks to the states

SHOCKS=[TREND]/LEVEL/BOTH

For TYPE=TREND, this determines whether the state space model includes a shock to the trend rate, a shock to the level (very rare choice), or both. The variance on the shock to the level frequently estimates zero.

Description

For TYPE=LEVEL, the three matrices are the (rather simple)

${\bf{A}} = [1],{\bf{C}} = [1],{\bf{F}} = [1]$

For TYPE=TREND, they are

${\bf{A}} = \left[ {\begin{array}{*{20}{c}}1 & 1 \\ 0 & 1 \\ \end{array}} \right],{\bf{C}} = \left[ {\begin{array}{*{20}{c}} 1 & 0 \\ \end{array}} \right],{\bf{F}} = \left[ {\begin{array}{*{20}{c}} 0 \\ 1 \\ \end{array}} \right],\left[ {\begin{array}{*{20}{c}} 1 \\ 0 \\ \end{array}} \right]\,{\rm{or}}\,\left[ {\begin{array}{*{20}{c}}1 & 0 \\ 0 & 1 \\ \end{array}} \right]$

where the ${\bf{F}}$ matrices are for the SHOCKS=TREND, SHOCKS=LEVEL and SHOCKS=BOTH options in order. The third of these requires two shocks on the state vector, while all other models require just one.

Example

From Harvey(1989), pp 89-90

open data purse.prn

data(format=prn,org=cols) 1 71 purse

* Estimate the local trend model. We first do this unconstrained.

nonlin sigsqeta sigsqeps sigsqzeta

compute sigsqzeta=.001

@localdlm(type=trend,a=a,c=c,f=f,shocks=both)

dlm(a=a,c=c,sv=sigsqeps,y=purse,sw=%diag(||sigsqeta,sigsqzeta||),f=f,exact,$

method=bfgs)

* Since that gives us a negative variance for zeta, we re-estimate,

* imposing the positivity restriction.

nonlin sigsqeta sigsqeps sigsqzeta sigsqzeta>=0.0

dlm(a=a,c=c,sv=sigsqeps,y=purse,sw=%diag(||sigsqeta,sigsqzeta||),f=f,exact,$

method=bfgs)