Table 3 presents results based on BP’s testing methodology. We have defined the upper bound to be 5 breaks. In the construction of the tests, we have allowed for heterogeneity and autocorrelation in the residuals, as well as different moment matrices for the regressors across segments. The Wdmax(1%) test, which tests the null hypothesis of no breaks against an unspecified number of breaks at the 99% level, is significant for all sectors except Consumer Staples. The supFT(l) test, evaluating a specified number of breaks versus the null of no breaks gives similar results. In particular the null of parameter constancy for all l breaks is rejected at the most conservative significance levels for all sectors with the exception of Consumer Staples, where once again no break is identified. The sequential tests also reject parameter constancy, although they give a mixed picture about the number of potential breaks. In particular, for the Consumer Discretionary, Technology, and Materials sectors the supFT(5|4) test rejects the null of 4 breaks, in favor of the 5 break alternative. The Industrials, Financials, and Utilities sectors are subject to 4 breaks, Healthcare to 3 breaks, while the Energy and Telecommunications sectors are subject to 2 breaks. Consumer Staples is the only sector where BP’s result points to the existence of a very stable relationship between our set of regressors and the sector’s returns.
(Insert Table 3 here)
While the above discussion is by no mean exhaustive, the instability of factor loadings and return variances for the chosen data is statistically established. We propose a model that we believe captures the dynamic nature of financial returns and their interaction with a pre-specified set of fundamental factors.
Bayesian Empirical Tests of the TVPFM
Specifications for Tested Models
With the factors for the TVPFM defined, the return generating process for each sector portfolio can now be presented as
ri,t1 0,t1 1,t1 ui,t ~ N(0, 2 ui,S t ).