Cotrending: Testing for common deterministic trends in varying means model

In a varying means model, the temporary evolution of a p-vector system is determined by p deterministic nonparametric functions superimposed by error terms, possibly dependent cross sectionally. The basic interest is in linear combinations across the p dimensions that make the deterministic functions constant over time. The number of such linearly independent linear combinations is referred to as a cotrending dimension, and their spanned space as a cotrending space. This work puts forward a framework to test statistically for cotrending dimension and space. Connections to principal component analysis and cointegration are also considered. Finally, a simulation study to assess the finite-sample performance of the proposed tests, and applications to several real data sets are also provided.