STARTEST Procedure

@STARTEST does an does an LM test for linearity vs an alternative of LSTAR or ESTAR (smooth transition autoregression) in a univariate autoregression. This was proposed by Terasvirta(1994). A similar test which can be used in more general situations than an autoregression is @RegSTRTest.

@StarTest( options ) y start end

Parameters

y	series to analyze
start, end	range of y to use. By default, the defined range of y

Options

D=delay on threshold variable [1]

P=lags in the autoregression [1]

TITLE=title for output ["Test for STAR in series ..."]

WEIGHTS=series of observation weights [equally weighted]

[PRINT]/NOPRINT

The WEIGHTS option can be used to adjust for outliers.

Sample Output

Test F-stat Signif

Linearity 1.3304417 0.2536

H01 0.9515415 0.4650

H02 1.6445252 0.1777

H03 1.3025990 0.2846

H12 1.5318647 0.1751

This is a table of tests of interaction terms between the regressors and powers (1, 2 and 3) of the threshold lag.

Linearity is the joint test of all the interaction terms

H01 is a test of the first order interaction terms only

H02 is a test of the second order interaction terms only

H03 is a test of the third order interaction terms only

H12 is a test of the first and second order interactions terms only

Either an LSTAR or ESTAR should cause rejection of linearity and rejection of H12. H12 is the appropriate statistic if ESTAR is the main hypothesis of interest. If H12 is rejected, but H03 is accepted, that points towards an ESTAR model, as opposed to an LSTAR. Note, however, that a rejection of linearity doesn't mean that you will be able to successfully fit any form of STAR model—all it says is that the linear model appears to be inadequate and that a STAR model might be a good alternative.

Example

* Enders, Applied Econometric Time Series, 4th edition

* Example from Section 7.9, pp 449-452

* STAR models

open data lstar.xls

data(format=xls,org=columns) 1 250 entry y

graph(footer="Figure 7.10 The Simulated LSTAR Process")

# y

stats y

@bjident y

linreg y

# constant y{1}

@regcorrs(number=12)

* This does the RESET test on the most recent regression.

@regreset(h=4)

* The STAR test can be done using the @STARTEST procedure. This does the

* regression described in the text and produces several test statistics.

* The non-linearity test is an F-test of the three non-linear terms. H12

* tests the joint significance of the squared and cubic terms and H03

* tests the signficance of the fourth degree term. If the model were

* ESTAR rather than LSTAR, the H03 would be expected to be insignificant.

@startest(p=1,d=1) y

@startest(p=1,d=2) y