On Fri, 14 Oct 2011, buehlerman wrote:

Thanks a lot for your immediate help and detailed explanation!

About one thing I'm not quite clear:

When the default fit = glm in gefp() is used:
sctest(gefp(Employed ~ Year + GNP.deflator + GNP + Armed.Forces, data =
longley, fit = lm), functional = meanL2BB)

To understand what exactly is tested, it may help to decompose this into the steps (1) model fitting, (2) process setup, (3) test statistic computation.

m <- lm(Employed ~ Year + GNP.deflator + GNP + Armed.Forces,
  data = longley)
p <- gefp(m, fit = NULL)
sctest(p, functional = meanL2BB)

To see which parameters are assessed you can look at

estfun(m)

or the corresponding fluctuation process

plot(p, aggregate = FALSE)

both of which have one column per parameter. The visualization for the Nyblom-Hansen test statistic

plot(p, functional = meanL2BB)

does not show the individual processes because you first aggregate across parameters using the squared Euclidian norm (before taking its mean).

is this then the original Nyblom's Parameter Stability Test (1989) or is it the joint (Nyblom-)Hansen test with theta = (beta) constant instead of theta = (beta, sigma^2) constant ?

The original Nyblom suggestion was for ML estimation of a distribution with one parameter (without covariates). Hansen extended this to the linear regression model and proposed to either compute one test statistic per parameter (which you can do with the "parm" argument of gefp) or a joint statistic for all parameters. Hansen included in "all" parameters also the variance, but the idea can be directly modified to any other model with a vector of parameters.

The reason that estfun(lm_object) does not include the variance is that coef(lm_object) and vcov(lm_object) etc. also do not include it. So it is the conceptual question whether lm() computes the OLS estimator or the full ML estimator. The normlm() wrapper on the ?DJIA man page is one possibility to switch to the ML view for the purposes of using "strucchange".

hth,
Z

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