We develop a framework to assess how successfully standard times eries models explain low-frequency variability of a data series. The low-frequency information is extracted by computing a finite number of weighted averages of the original data, where the weights are low-frequency trigonometric...

We develop a framework to assess how successfully standard times eries models explain low-frequency variability of a data series. The low-frequency information is extracted by computing a finite number of weighted averages of the original data, where the weights are low-frequency trigonometric...

We propose a multivariate simultaneous unobserved components framework to determine the two-sided interactions between structural trend and cycle innovations. We relax the standard assumption in unobserved components models that trends are only driven by permanent shocks and cycles are only...