We develop a new parameter instability test against the alternative of a time-varying parameter. The new test generalizes the seminal ARCH-LM test for a constant variance against the alternative of autoregressive conditional heteroskedasticity to settings with nonlinear time-varying parameters and non-Gaussian distributions. These alternative model settings are unified by the class of score-driven time-varying parameter models. We discuss the performance of our test compared to classic but also to more recent alternative tests, including tests against structural breaks and parameter-driven dynamics. For regime switching and mean-reverting parameter-driven dynamics, the new test has higher and more stable power properties. For more local alternatives and for structural breaks, the recent test by Müller and Petalas (2010) performs best. We provide an application to a heavily unbalanced panel of losses given default for U.S. corporations from 1982 to 2010 and provide evidence of significant parameter instability in the parameters of a static beta distributed model.

The Volume Weighted Average Price (VWAP) mixes volumes and prices at intra-daily intervals and is a benchmark measure frequently used to evaluate a trader's performance. Under suitable assumptions, splitting a daily order according to ex-ante volume predictions is a good strategy to replicate the VWAP. To bypass possible problems generated by local trends in volumes, we propose a novel Generalized Autoregressive Score (GAS) model for predicting volume shares (relative to the daily total), inspired by the empirical regularities of the observed series (intra-daily periodicity pattern, residual serial dependence). An application to six NYSE tickers confirms the suitability of the model proposed in capturing the features of intra-daily dynamics of volume shares.

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