Seasonal unit root characteristics of disaggregated output

Tests for unit roots and cointegration have been extended to enable tests for seasonal units and more importantly tests for seasonal cointegration between series with common seasonals. To this end seasonal unit root tests are applied to unadjusted New Zealand GDP data and its disaggregated components. These, tests reveal that while aggregate GDP clearly exhibits a constant seasonal pattern a majority of its component series exhibit a changing seasonal pattern implying that stochastic innovations are occurring at the seasonal frequency. Furthermore, seasonal cointegration tests reveal that these changing seasonal patterns, observed in the component series, cancel out yielding a deterministic seasonal pattern on aggregation.