Effects of outliers on two nonlinearity tests

Two Lagrange multiplier tests for time series nonlinearities in the presence of outliers are examined by simulation experiments. The nonlinearities studied are autoregressive conditional heteroskedasticity (ARCH) and bilinearity; the outlier types are additive, innovative, temporary change and reallocation outliers. The results show that both the sizes and powers of the tests can be severely distorted by even a single outlier. The severity of the distortions depends on the outlier type and magnitude, but also on the underlying process generating the series.