Bayesian estimation of a shift point in a two-phase regression model
Streszczenie
The purpose of this paper is to carry out the Bayesian analysis of
a two-phase regression model with an unknown break point. Essentially, there are two
problems associated with a changing linear model. Firstly, one will want to be able to
detect a break point, and secondly, assuming that a change has occurred, to be able
to estimate it as well as other parameters of the model. Much of the classical testing
procedure for the parameter constancy (as the Chow test, CUSUM, CUSUMSQ, tests
and their modifications, predictions tests for structural stability) indicate only that the
regression coefficients shifted, without specifying a break point.
In this study we adopt the Bayesian methodology of investigating structural changes
in regression models. The break point is identified as the largest posterior mass density,
the peak of the posterior discrete distribution of a break point. It seems to work well
with artificially generated data.
The Bayesian framework also seems to be promising for extending the analysis of
a single break to that of multiple breaks.
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