The Influence of Additive Outliers on the Performance of Information Criteria to Detect Nonlinearity

In this paper the performance of information criteria and a test against SETAR nonlinearity for outlier contaminated time series are investigated. Additive outliers can seriously influence the properties of the underlying time series and hence of linearity tests, resulting in spurious test decisions of nonlinearity. Using simulation studies, the performance of the information criteria SIC and WIC as an alternative to linearity tests are assessed in time series with different degrees of persistence and different outlier magnitudes. For uncontaminated series and a small sample size the performance of SIC and WIC is similar to the performance of the linearity test at the $5\%$ and $10\%$ significance level, respectively. For an increasing number of observations the size of SIC and WIC tends to zero. In contaminated series the size of the test and of the information criteria increases with the outlier magnitude and the degree of persistence. SIC and WIC clearly outperform the test in larger samples and larger outlier magnitudes. The power of the test and of the information criteria depends on the sample size and on the difference between the regimes. The more distinct the regimes and the larger the sample, the higher is the power. Additive outliers decrease the power in distinct regimes in small samples and in intermediate regimes in large samples, but increase the power in similar regimes. Due to their higher robustness in terms of size, information criteria are a valuable alternative to linearity tests in outlier contaminated time series.