This paper provides analyses of multivariate daily immigration data, separating the long-term trend from annual and weekly patterns of seasonality via the use of so-called canonical models in an unobserved components framework. These canonical models are as stable as possible, having the maximal amount of white noise already removed, resulting in a less variable stochastic component. To further separate trend and annual seasonality, we employ a Hodrick-Prescott (HP) filter to the combined component, and using an implied models framework determine the uncertainty. To surmount the computational challenges, we implement forecast extension together with application of a bi-infinite filter composed of the HP and model-based aspects. Parameter estimates are obtained by a simple method-of-moments estimator, which is modified to ensure that no spurious co-integration effects are present in the model. These methods are demonstrated on the six high frequency immigration series, successfully decomposing