The Hodrick-Prescott filter applied to seasonally adjusted series has become a paradigm for business-cycle estimation at many economic agencies and institutions. We show that the filter can be obtained from MMSE estimation of the components in an unobserved component model, where the original...

Programs TRAMO and SEATS, that contain an ARIMA-model-based methodology, are applied for seasonal adjustment and trend-cycle estimation of the exports, imports, and balance of trade Japanese series. The programs are used in an automatic mode, and the results are found satisfactory. It is shown...

The ARIMA model based methodology of programs TRAMO and SEATS for seasonal adjustment and trend cycle estimation was applied to the exports, imports, and balance of trade Japanese series in Maravall (2002). The programs were used in an automatic mode, and the results analyzed. The present paper...

In the analysis of time series, it is frequent to classify perturbations as Additive Outliers (AO), Innovative Outliers (IO), Level Shift (LS) outliers or Transitory Change (TC) outliers. In this paper, a new outlier type, the Seasonal Level Shift (SLS), is introduced in order to complete the...

The paper deals with estimation of missing observations in possibly nonstationary ARIMA models. First, the model is assumed known, and the structure of the interpolation filter is analysed. Using the inverse or dual autocorrelation function it is seen how estimation of a missing observation is...

Maravall and del Río (2001), analized the time aggregation properties of the Hodrick-Prescott (HP) filter, which decomposes a time series into trend and cycle, for the case of annual, quarterly, and monthly data, and showed that aggregation of the disaggregate component cannot be obtained as...

Filters used to estimate unobserved components in time series are often designed on a priori grounds, so as to capture the frequencies associated with the component. A limitation of these filters is that they may yield spurious results. The danger can be avoided if the so called ARIMA model...

This paper applies the programs TRAMO and SEATS to seasonal adjustment of the monthly Consumer Price Index Swiss series. It is shown how the results of the purely automatic procedure can be improved with two simple modifications: one that emerges from the TRAMO-SEATS diagnostics, and another...

The Seasonal Adjustment Research Appraisal committee was created in Italy to evaluate procedures for seasonal adjustment of economic series. Because the TRAMO-SEATS programs were one of the main procedures considered, the committee sent a selection of 11 series of interest to be analysed. This...

Brief summaries and user instruction are presented for the programs TRAMO ("Time Series regression with ARIMA Noise, Missing Observations and Outlers") and SEATS ("Signal Extraction in ARIMA Time Series").