Testing for Parameter Instability across Different Modeling Frameworks

We develop a new parameter instability test that generalizes the seminal ARCH-Lagrange Multiplier test of Engle (1982) for a constant variance against the alternative of autoregressive conditional heteroskedasticity to settings with nonlinear time-varying parameters and non-Gaussian distributions. We investigate the performance of the new test relative to both classic and recently proposed parameter instability tests, including tests against structural breaks and parameter-driven dynamics. We find that the recent test of Müller and Petalas (2010) performs best across a wide range of alternatives, particularly if parameter instability is slow. For time-varying parameters that exhibit more mean reversion, our new test has higher power. We provide an application to a heavily unbalanced panel of losses given default for US corporations from 1982 to 2010 and provide evidence of significant parameter instability in the parameters of a static beta distributed model.