Testing for parameter instability in competing modeling frameworks

We develop a new parameter stability test against the alternative of observation driven generalized autoregressive score dynamics. The new test generalizes the ARCH-LM test of Engle (1982) to settings beyond time-varying volatility and exploits any autocorrelation in the likelihood scores under the alternative. We compare the test's performance with that of alternative tests developed for competing time-varying parameter frameworks, such as structural breaks and observation driven parameter dynamics. The new test has higher and more stable power against alternatives with frequent regime switches or with nonlocal parameter driven time-variation. For parameter driven time variation close to the null or for infrequent structural changes, the test of Müller and Petalas (2010) performs best overall. We apply all tests empirically to a panel of losses given default over the period 1982 - 2010 and find significant evidence of parameter variation in the underlying beta distribution.