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 non-local parameter driven time-variation. For parameter driven time variation close to the null or for infrequent structural changes, the test of Muller 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.
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