starTest#

Purpose#

Estimates a p^th order threshold autoregression and tests the hypothesis of a linear autoregression, using the statistics described in “Inference when a nuisance parameter is not identified under the null hypothesis.” (Hansen, 1996).

Format#

{ s3, p3 } = starTest(yt, p, omit)#

Parameters:

yt (matrix) – Nx1 data.
p (scalar) – autoregressive order of the TAR model.
omit (scalar or vector) – lags (below p) to omit from autoregression [0 implies an AR(p)].

Returns:

s3 (scalar) – value of the LM test statistic.
p3 (scalar) – p-value of s3.

Example#

new;
cls;
library tsmt;

// Real GNP data
// Seasonally adjusted and transformed in annualized quarterly growth rates
gnp = loadd( getGAUSSHome() $+ "pkgs/tsmt/examples/gnp_4790.fmt");
yg = ln( gnp[., 1] );
y = (yg[2:rows(yg)]-yg[1:rows(yg)-1])*400;

// Maximum number of lags considered
p = 5;

// Lags to omit from the test
omit = { 3, 4 };

{ s3, p3 } = starTest( y, p, omit );

// Print results
print "LM statistic :";; s3;
print;
print "P-value :";; p3;

References#

Hansen, B.E. (1996). Inference when a nuisance parameter is not identified under the null hypothesis, Econometrica, 64(2), 413-430.
Franses, P.H. and Dijk, D. (2000) Non-linear Time Series Models in Empirical Finance. Cambridge University Press, New York.

Library#

tsmt

Source#

startest.src