LOCALDLMINIT Procedure

@LocalDLMInit provides rough estimates of the component variances for the irregular and trend rate variances for a local level or local trend model, possibly in the presence of seasonals.

@LocalDLMInit(options) series start end

Parameters

series	observable series
start, end	range over which to compute approximate variables. By default, the defined range of series.

Options

DESEASONALIZE/[NODEASONALIZE]

chooses whether to remove seasonal (by regression on dummies) first.

IRREGULAR=(output) estimate of the irregular (measurement error) variance

TREND=(output) estimate of the trend rate variance

Example

This does a local trend state-space model of log GDP, first by using the Hodrick-Prescott filter (which is a special case with a specific variance ratio), then by freely estimating the component variances. For the latter, @LocalDLM is used to set up the system matrices for the state-space model, then @LocalDLMInit is used to get preliminary estimates of the variances. DLM does the actual estimation.

* Martin, Hurn, Harris, "Econometric Modelling with Time Series"

* Application 15.8.1, from pp 567-571

* Hodrick-Prescott filter

open data "usgdp.dat"

calendar(q) 1940:1

data(format=prn,nolabels,org=columns) 1940:01 2000:01 usgdp

set logy = 100.0*log(usgdp)

* This is how you would HP-filter a data series using RATS

filter(type=hp) logy / hplogy

graph(footer="Figure 15.4 Log of GDP with smoothed trend component",$

key=upleft,klabels=||"Smoothed","Actual"||) 2

# hplogy 1940:1 1952:4

# logy 1940:1 1952:4

* This does the analysis by Kalman filtering

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

@localdlminit(trend=sigsqzeta,irreg=sigsqc) logy

* Freely estimate both component variances

nonlin sigc sigzeta

compute sigc=sqrt(sigsqc),sigzeta=sqrt(sigsqzeta)

dlm(presample=diffuse,a=a,c=c,f=f,sv=sigc^2,sw=sigzeta^2,y=logy,type=smooth,$

method=bfgs) / xstates