A Comparison of the Runs Test for Volatility Forecastability and the LM Test for GARCH Using Aggregated Returns

Christoffersen and Diebold (2000) have introduced a runs test for forecastable volatility in aggregated returns. In this note, we compare the size and power of their runs test and the more conventional LM test for GARCH by Monte Carlo simulation. When the true daily process is GARCH, EGARCH, or stochastic volatility, the LM test has better power than the runs test for the moderate-horizon returns considered by Christoffersen and Diebold. For long-horizon returns, however, the tests have very similar power. We also consider a qualitative threshold GARCH model. For this process, we find that the runs test has greater power than the LM test. Theresults support the use of the runs test with aggregated returns.