Before we estimate and evaluate the model in detail, we proceed with an exploratory investigation of the time varying properties of the data. We are interested in making some general statements regarding the stability of a static version of our model with respect both to the exposures to the macroeconomic state variables and the error variance. A sufficient condition for proposing a dynamic model that explicitly incorporates time-variation in the parameters relating financial returns to macroeconomic variables is to show that its static counterpart is unstable, i.e., the parameters are subject to structural change. Thus, our purpose is to test for regression stability without explicitly estimating the timing of the breaks or the value of the parameters. A variety of means for testing and estimating structural break models have been proposed in the literature. We concentrate on the testing frameworks developed by Hansen (1992) and Bai and Perron (1998, 2001), BP hereafter. Bayesian model selection techniques are explored in a later section.
Hansen’s Lc statistic is a Lagrange multiplier test of the null hypothesis of constant parameters against the alternative that parameters follow a martingale. The test relies on the assumption of
presented at the beginning of this section. As in Hansen (1992), we are interested in testing the stability of each parameter individually, as well as the joint stability of the parameters in each of the sector regressions. Hansen provides the critical values for these tests.
BP developed a method for estimating multiple structural breaks in linear regression models. Their testing procedure allows for differentiation in the regression errors, but does not provide methods for parametrically estimating this heterogeneity. The determination of break points depends on both the distance allowed between break points, as well as the upper bound imposed in the number of breaks to be considered. The latter point is less of a drawback in the present context as we are only interested in testing for the presence of parameter instability. In BP’s methodology there is not a unique test that determines the number of breaks. The statistical determination of structural change depends on the values of various test statistics. The first one is the supFT(l) test which tests the null hypothesis of no breaks for all the parameters, against the
of future returns. Ferson and Harvey (1999) use the term spread, dividend yield and default spread as instruments in