Abstract
In seasonal adjustment a time series is considered as a juxtaposition of several components, the trend-cycle, and the seasonal and irregular components. The Bureau of the Census X-11 method, based on moving averages, correction of large errors and trading day adjustments, has long dominated. With the success of ARIMA modelling at the end of the 20th century, methods with better outlier detection and trading day corrections by regression with ARIMA errors have appeared, with the regARIMA module of Census X-12-ARIMA or Bank of Spain TRAMO-SEATS. SEATS consists of extracting the components by an ARIMA-model-based unobserved components approach. This means that models are used for each component such that the sum of the components is compatible with the ARIMA model for the corrected time series. The underlying theory of the SEATS program is studied in many papers but there is no complete and systematic description of its output. Our purpose is to examine SEATS text output and to explain the results in simple words and formulas. This is done on a simple example, a time series with a non-seasonal model so that the computations can be verified step by step. The principles behind SEATS are first described, including the admissible decompositions and the canonical decomposition, and the derivation of the Wiener-Kolmogorov filter. Then the example is introduced: the interest rates of US certificates of deposits. The text output from SEATS is presented in edited form in several tables. Finally, the main results are checked on the example by means of a Microsoft Excel workbook and direct computations. In particular, the forecasts and backcasts are obtained; the admissible and canonical decompositions with two components are discussed; the filters are first derived using autocorrelations of two auxiliary ARMA processes, then applied on the prolonged time series; and the characteristics of the estimates, the revisions and the growth rates are analyzed.
Highlights
Seasonal adjustment is fundamental for the analysis and interpretation of macroeconomic time series
In the Excel file, worksheet Second, we can check on the example, by changing the MA coefficient in cell G12 so that the canonical decomposition corresponds to the case where the minimum of the spectrum of the permanent or trend component is equal to 0, see Fig. 2
SEATS is essential for seasonal adjustment since it is used in both Bureau of the Census X-13ARIMA-SEATS and Bank of Spain TRAMO-SEATS, the main two software packages for seasonal adjustment
Summary
Seasonal adjustment is fundamental for the analysis and interpretation of macroeconomic time series. (Time Series Research Staff 2013), the Bureau of the Census X-13ARIMA-SEATS has appeared, with few changes on regARIMA and automdl, but offering a choice between SEATS and the old X-11 decomposition procedure, with some improvements for the latter. The main purpose of this paper is to examine the details of SEATS text output and to explain the results in simple words and formulas. It is done on the basis of an example, with a step-by-step description of a typical output from SEATS. Appendix 2 will introduce the spectral analysis used in SEATS for the derivation of a canonical decomposition
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