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...

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...

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...

Present practice in applied time series work, mostly at economic policy or data producing agencies, relies heavily on using moving average filters to estimate unobserved components in time series, such as the seasonally adjusted series, the trend, or the cycle. The purpose of the present paper...

In this monograph, first, we analyze in detail some of the major limitations of the standard procedure to estimate business cycles with the Hodrick-Prescott (HP) filter. By incorporating time series analysis techniques, it is seen how some intuitive and relatively simple modifications to the...

Hodrick-Prescott (HP) Filter of (most often, seasonally adjusted) quaterly series is analysed. Some of the criticism to the filter are adressed. It is seen that, while filtering strongly affects autocorrelations, it has little effect on crosscorrelations. It is argued that the criticism that HP...

The paper details an application of programs TRAMO and SEATS to seasonal adjustment and trend-cycle estimation. The series considered is the German Retail Trade Turnover series, for which, when adjusting with X12-ARIMA, the Bundesbank had identified two problems. One had to do with...

The problem of optimal estimation of missing observations in stationary Autoregressive Moving Average (ARMA) models was solved in Jones (1980). Extension of his aproach to nonstationary integrated ARMA (i.e., ARIMA) models posed serious problems, having mostly' to do with the specification of...

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...