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Abstract:
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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 the data into diverse components that each have correct (and disjoint) dynamic properties.
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