Summary

Seasonal adjustment, which consists in the estimation and the removal of the seasonal variation from time series has a long tradition, documented in Zellner (1978), Hylleberg (1992) and, more recently, Bell, Holan and McElroy (2012). Since both seasonally adjusted series and seasonal component are unobserved components and, consequently, a given time series has an unknown composition, many methods and procedures have been proposed and implemented to perform the seasonal adjustment. In addition to the ARIMA-model based method, implemented in TRAMO-SEATS (Maravall, 2012) and to the moving average based method implemented in X-12-ARIMA (U.S. Census Bureau, 2012), seasonal adjustment may be performed by some more or less conventional methods, such as Structural Time Series (STS) models, Bayesian seasonal adjustment, signal-extraction methods, different nonparametric (like spline-based) methods etc. Although the two main-stream procedures, TRAMOSEATS and X-12-ARIMA, are generally recognized and accepted as the leading procedures in a process of production of seasonally adjusted data in official statistics, it is still important to study the alternatives in order to encourage diversity in development of seasonal adjustment.

An outline of the several seasonal adjustment procedures used at the National Statistical Offices of the European Union is given in Fischer (1995). Although this document might look outdated it still contains interesting comparisons among several methods used in different national institutes in Europe. This document emphasizes advantages of TRAMO-SEATS and X-12-ARIMA over the comparing methods DAINTIES, BV4, SABL, X-11 UK version and X-11-ARIMA. Note that some of the methods described in the document are no longer in use.

Since the time of publication of the mentioned document several new methods for seasonal adjustment have been proposed in the available literature. These methods arise because of the need to deal with some issues that ARIMA-model based methodologies have difficulty tackling. Real time signal extraction is one such methodology based on the Direct Filter Approach (Wildy, 2008), implemented in the R-package signal extraction (R Development Core Team, 2012) created by the same author. The author claims that this method has certain advantages over the ARIMA-model based methods with respect to the turning-point detection and other relevant timing issues.

Non-parametric methods such as STL allegedly generate robust estimates of the time series components not distorted by aberrant observations (outliers). See Cleveland (1990) and R-package STL for more details (R Development Core Team, 2012). Although robust to outliers, the STL-method has some disadvantages in official statistics. This procedure does not have full functionality needed to produce seasonally adjusted estimates in a way relevant to a government statistical agency. Furthermore, the development of this method seems to be stagnated during recent years.

Bayesian seasonal adjustment, originally proposed by Akaike (1980), has been developed and implemented in several software-platforms, such as R-package TIMSAC and SAS procedure TSBAYSEA (SAS Institute, 2009). However, such a methodology has not yet attracted attention of the national statistical institutes, due to its complexity and the required theoretical background necessary to deal with the Bayesian framework.

One of the alternative modelling frameworks, the STS-models, is recommended as a substitute to the two main methods in the ESS (European Statistical System) guidelines on seasonal adjustment (Eurostat, 2009), if certain conditions are satisfied. The use of some other alternative methods falls under the category "to be avoided".

The ESS guidelines on seasonal adjustment aim to achieve harmonisation of the member state’s national practices by promoting the idea of best practices in seasonal adjustment. Although the guidelines work towards a unified framework for seasonal adjustment within the ESS, they are not supposed to put limitations on the use of other methods. Under appropriate circumstances some less conventional models might offer innovative solutions to certain re-occurring problems that the national statistical institutes (NSI) have to deal with in their daily work with seasonal adjustment.

The main focus of this module is put on description of the decomposition based on ARIMA models, on moving averages and on STS-models, while the other classes of models are not treated. Section 2 is organized as follows. Sections 2.1 and 2.2 describe the two main stages of the seasonal adjustment of a given time series through the most widespread procedures, i.e., TRAMO-SEATS and X-12-ARIMA (X-13-ARIMA-SEATS): the pre-treatment and the decomposition. In particular, section 2.1 deals with the pre-treatment of time series required by both procedures before the decomposition and section 2.2 gives an overview of the decomposition based on moving averages (or ad hoc filters) and ARIMA models. Section 2.3 presents the STS model based approach, highlighting features that make it an appealing tool for seasonal adjustment. Finally, referring to TRAMO-SEATS and X-12-ARIMA, section 2.4 details the seasonal adjustment process of time series, distinguishing and describing eight steps.

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