We describe a simple procedure for decomposing a vector oftime series into trend, cycle, seasanal and irregular components. Contrary to corumon practice, we do nol assume these components to be orthogonal conditional on their past. However, tbe state-space representation employed assures that their smoothed estimates converge to exact vaIues, with null variances and covariances. Among ather implications, this means that the components are n01 revised when the sample ¡nereases. The practica! application of the method is illustrated both with simulated and real data.Keywords: State-space models, seasonal adjustment, trends, unobserved components.JEL Classification: C32, CS3, E27, E37 r>¡fOlq~)<'i'7 . b meaoS of a differential equatio n , designed to Ad-hoc methods consist of filtering the senes Y . usly chosen frequencies. The most . k f spectral power at preVIo extractthecomponentsgeneratingpea so. e x 11 saga, see Shlskin etal. (1967) and h ' imation are tn the ensusfamous examples oft IS appro x . l' d' t end extractíon is the HP filter, due to ) An 'nf1 ential proposal specla lze m r . Findley et al. (1998 ARIl\.1A processes for each UC, constrained that their sum is observationany equivalent to the reducedfonnmodel.The FD approach is due to Box et al. (1987), for a recent paper on FD see Espasa and Peña (1995). It consists of decomposing the h-steps-ahead forecast function of a given univañate model, generally belonging to the ARIMA family, into persistent and transitory components, wruch can also be broken down into seasonal and nonseasonal terms.Last, STSM are directIy set up in terms ofthe components in (1), which are represented by statespace (from now on SS) models specified according to the statistical properties ofthe time series, see Engle (1978), Harvey (1989), Harvey and Shephard (1993) and Young el al. (1999). Whereas AME and FD techniques are essentially urnvariate, the simpler structure of SS models makes it easy to define STSM for vectors oftime series and allows extensions to nonlinear and non-gausslan systems or models with stochastic vanances. This approach is implemented with sorne differences in three main software packages: MICRO-CAPTAIN, see Young and Brenner (1991), BATS, see Pole et al. (1994), and STAMP, see and Koopman et al. (1995).Once the models for the components have been specified and estimated using any of these methodologies, thefinal step in the analysis consists of estimating the components. To this purpose most approaches use a c1ass of algorithms known in general as "symmetric filters" such as, e.g_, the WienerKolmogorov filter, see Burman (1980) and Bell and llillmer (1984), and the fixed-interval smoother, see Anderson and Moare (1979). The word "symmetric" aHudes to the fact that current estimates ofthe components depend on past and future values ofthe time series. FD methods are an important exception to tbis general approach, because the components implied by a forecast function depend only on past sample values and, therefore, one-side asyrnmetric filters ...

No abstract

No abstract

This paper discusses how to determine the order of a state-space model. To do so, we start by revising existing approaches and find in them three basic shortcomings: i) some of them have a poor performance in short samples, ii) most of them are not robust and iii) none of them can accommodate seasonality. We tackle the first two issues by proposing new and refined criteria. The third issue is dealt with by decomposing the system into regular and seasonal subsystems. The performance of all the procedures considered is analyzed through Monte Carlo simulations.

No abstract