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29.1.        Introduction. The present chapter explains the concept of seasonal adjustment of data, its key features and main approaches, including revision policy and quality issues in general terms. It then provides some examples of country practices in the application of seasonal adjustments to international merchandise trade data. It is based on IMTS 2010 (para. 11.3), which encourages countries to compile and publish, where appropriate, seasonally adjusted monthly and quarterly international merchandise trade data on a regular basis. It is related to chapter XXVI on dissemination.

A.        Basic concepts and uses of seasonally adjusted trade data

29.2.        Need for seasonally adjusted data. Monthly and quarterly data on international merchandise trade statistics are an important tool for economic policymaking, business cycle analysis, modelling and forecasting. However, they are often characterized by seasonal fluctuations and other calendar or trading-day effects, which mask other characteristics of the data which are of interest to analysts. Seasonal adjustment is a process of estimating and removing seasonal or calendar influences from a time series in order to achieve a better knowledge of the underlying behaviour.

29.3.        Seasonal adjustment method. Because national circumstances vary from one country to another, no preferred seasonal adjustment method is recommended. If seasonally adjusted data are published, it is recommended that information on the adjustment methods be provided by countries in their metadata (IMTS 2010, para. 11.4).

29.4.        Concept of seasonal adjustment. Seasonal adjustment is the process of estimating and removing effects in a sub-annual time series that occur at about the same time and magnitude each year, as well as calendar-related systematic effects that are not stable in annual timing, which are often large enough to mask other data characteristics. Removing the seasonal component allows for an easier comparison of long- and short-term movements across sectors and countries and further contributes to an understanding of the non-seasonal behaviour which is often of interest for economic policymaking, business cycle analysis, modelling and forecasting.

29.5.        Components of time series. A time series is generally considered to consist of trend, cycle, seasonal and irregular components. The trend, cycle and irregular components together reflect long-term movements lasting many years, fluctuations relating to the business cycle, and unforeseeable movements of all kinds. The seasonal component of a time series represents the movement within the year, and includes the effect of climatic and institutional events that are repeated regularly throughout the year, as well as calendar-related systematic effects that are not stable in annual timing, such as trading-day and moving holiday effects. Seasonal adjustment is the process of completely eliminating the seasonal component from the original time series.

29.6.        Tools used for seasonal adjustment. Seasonal adjustment is typically accomplished with the assistance of free and publicly available software packages, the most widespread of which are TRAMO-SEATS (supported by the Bank of Spain) and X-12-ARIMA (supported by the United States Census Bureau).[1] As the seasonal component is not precisely defined, seasonal adjustment often depends on the a priori hypotheses underlying the model chosen and upon the software and specifications chosen.

B.        Preliminary treatment of data prior to seasonal adjustment

29.7.        Seasonal adjustment begins with a preliminary process of identifying and removing outliers, adjusting for those calendar effects that are not stable in annual timing, and identifying an appropriate decomposition type. 

29.8.         Graphical analysis. Preliminary treatment of the data should begin with a graphical analysis of the series in order to identify potential problems with the data, select appropriate parameters, and determine how to perform the seasonal adjustment. Relevant preliminary graphical analysis should examine the length of the series, the presence of strange values, the structure of the series, the presence of possible breaks in seasonality, and the decompositions scheme. 

29.9.        Outliers. Since most seasonal adjustment methods use procedures and filters that are sensitive to outliers, these should be identified and removed before estimating the seasonal components. Outliers clearly due to errors in the data should be discarded. However, since outliers not due to error typically contain information about key events, these should be reintroduced into the data after seasonal adjustment. 

29.10.    Calendar effects. Calendar effects are regular effects that do not necessarily occur in the same month or quarter each year but that can be identified and removed from the series. These effects include holidays whose exact timing shifts systematically each calendar year and the variation in the number of times each day of the week occurs in a given month or quarter. These effects must be corrected for using standard seasonal adjustment tools, so as to prefent mis-specification of the model or a compromising of the overall quality of seasonal adjustment. The decision to correct for other effects, such as temperature, school holidays or bridge holidays, should be made on a case-by-case basis. 

29.11.    Decomposition. The decomposition scheme specifies how the trend-cycle, seasonal and irregular components combine to form the original series. Additive decomposition assumes that the components of the time series behave independently of each other. In particular, the size of the seasonal oscillations is independent of the level of the series. Multiplicative decomposition, often chosen by default in seasonal adjustment software packages, assumes that the components of the series are interdependent and thus that the size of the seasonal variation increases and decreases with the level of the series.

C.        Seasonal adjustment

29.12.    Choice of seasonal adjustment approach. TRAMO-SEATS and X-12-ARIMA are currently the most commonly used seasonal adjustment approaches. TRAMO-SEATS is based on a parametric approach (where the model structure is specified a priori), while X-12-ARIMA is based on a non-parametric approach (where the model structure is determined from the data). A third possible approach is to use structural time-series models, provided that they allow for a complete calendar and outlier treatment and include an adequate set of diagnostics. The consistent use of a common set of seasonal adjustment packages will improve transparency and comparability of seasonally adjusted time-series across countries.

29.13.    Seasonal adjustment and consistency with annual data. Annual trade totals based on seasonal adjustment will not automatically (or conceptually) be equal to the corresponding annual trade totals based on unadjusted data. Specifically, the annual totals of the unadjusted series and the seasonally adjusted series will be equal only when the series are adjusted additively, the seasonal pattern is fixed from one year to the next, and there are no trading-day adjustments. The impact of working days, moving holidays and other calendar effects change from one year to the next. Moving seasonality also implies that the impact of the seasonal effect will vary across years. Nonetheless, the process of ensuring that seasonally adjusted values sum to their unadjusted annual values, known as benchmarking, can be conducted using seasonal adjustment software.

29.14.    Direct versus indirect seasonal adjustment. Direct seasonal adjustment is performed if all time series, including aggregates, are seasonally adjusted on an individual basis. Indirect seasonal adjustment is performed if the seasonally adjusted estimate for a time series is derived by combining the estimates for two or more directly adjusted series. Indirect seasonal adjustment should be preferred when the component series that makes up the aggregate series have both distinctively dissimilar seasonal patterns and adjustments of good quality. Direct seasonal adjustment should be the approach of choice when the corresponding series have similar seasonal patterns and summing the series may reduce the amount of unexplained variation.[2]

D.        Revision policies

29.15.    Reasons for revisions to seasonally adjusted data. Revisions of seasonally adjusted data occur for two main reasons. Seasonally adjusted data may be revised as the consequence of a revision of the unadjusted data, which may be the result of an improvement in the information set. Revisions of seasonally adjusted data can also occur because of a better estimate of the seasonal pattern due to new information provided by new unadjusted data and to the characteristics of the filters and procedures for removing seasonal and calendar components. The challenge is to strike a balance between the precision of seasonally adjusted data and their stability over time. Revisions of seasonally adjusted data should be carried out in accordance with a coherent, transparent and officially announced revision policy, and should not be more frequent than the revisions to the raw data. In this regard, it is good practice to keep the model specification for seasonal adjustment as stable as possible over time, and to coordinate the timing of revisions to the model specification with the timing of major revisions of the raw data.

29.16.    Trade-off between frequency and accuracy. How seasonal adjustment is carried out has implications for the revision policies. At one extreme, there is so-called current adjustment, which minimizes the frequency of revisions and concentrates the revisions mainly within a predefined review period. At the other extreme, there is so-called concurrent adjustment, which maximizes the accuracy of the adjusted data at any given point, but leads to more revisions, often from the beginning of a series, with many of them small and moving in opposite directions. In practice, other procedures are utilized, based on a combination of these two extreme approaches.

29.17.    The decision regarding whether a changed time series should be published in its entirety is influenced by several factors. On the one hand, there is an incentive from a methodological perspective to treat all values identically, so as to ensure that calculations are easy to understand and to replicate. However, it is nevertheless questionable whether a newly added figure actually contains information relevant for significant revisions to the estimation of the usual seasonal fluctuations in previous decades. As a means of balancing the information gain and the revision horizon, the revision period for the seasonally adjusted data is often limited to being between three and four years longer than the revision period for the unadjusted data (see also para. 26.15).

E.        Quality of seasonal adjustment

29.18.    Absence of residual seasonality. The most fundamental requirement of seasonal adjustment is that there be no estimable seasonal effect, known as residual seasonality, still present in the seasonally adjusted series. To detect residual seasonality and residual trading-day effects, validation should be performed using spectral diagnostics as well as other tools included in the seasonal adjustment packages, perhaps complemented by graphical diagnostics and statistical tests from external statistical packages. Both TRAMO-SEATS and X-12-ARIMA provide a wide range of quality measures and diagnostics for this purpose.

29.19.    Stability and lack of bias. Other important requirements for good seasonal adjustment are a lack of bias in the level of the series and stability of the estimates. A lack of bias implies that the level of the seasonally adjusted series is similar to the level of the original series. Stability of the estimates implies that the inclusion of new data into the estimation procedures will not result in large changes in the estimates. Large revisions can indicate that the estimates are misleading or even meaningless.

F.        Specific issues

29.20.    Length of series. A series that is under three years in length cannot be seasonally adjusted accurately with either TRAMO-SEATS or X-12-ARIMA. It is possible, however, to adjust these series using alternative, less standard, procedures. For series that are long enough to run X-12-ARIMA or TRAMO-SEATS but remain quite short (three to seven years), some instability problems can araise. Several empirical comparisons have been carried out to assess the relative performance of X-12-ARIMA and of TRAMO-SEATS on short time-series.

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29.22.    Series requiring non-standard seasonal adjustment. Some series can be characterized by highly specific features which preclude the application of standard seasonal adjustment methods. Such features include high non-linearity[3], absence of a clear signal due to a dominant irregular component, unstable seasonality, a high number of outliers, and heteroskedasticity.[4] In such cases, ad hoc treatment should be carried out.

G.        Data presentation

29.23.    Data can typically be presented in raw, seasonally adjusted, calendar-adjusted only or trend-cycle form. The raw data contain all the characteristics of the time series. As the seasonally adjusted data contain the trend-cycle and the irregular components, they contain the “news” of the series. Much of the discussion on trend-cycle analysis focuses on the so-called end-point problem. Since the trend-cycle values at the end of the series are usually estimated by extrapolation, the estimated trend-cycle for the most recent data is very uncertain and can suffer from phase-shift[5] problems. Particular care is required at turning points, where it often takes months until the new correct direction of development appears. In addition, it is good practice to monitor discrepancies between the trend of raw data and the trend of seasonally adjusted data

29.24.    In all cases, the information contained within the press release should reflect the principles of ensuring transparency and assisting users in making informed decisions.

H.        Country examples

29.25.    Example of Germany. InGermany, the seasonal adjustment of foreign trade data as well as of other important economic indicators entails close collaboration between the Central Bank and the Federal Statistical Office. The original data collected by the Federal Statistical Office are seasonally adjusted and calendar-adjusted by both institutions using the same X-12-ARIMA procedure (which represents the evolution of the well-known X-11 model developed by the United States Bureau of the Census). As a second step, both institutions examine the results and have to decide in common whether any of the processing parameters that are crucial for the quality of the results have to be adjusted or not. In the case where the parameters are changed, the calculation of seasonally adjusted figures is repeated by both institutions. In this way each institution verifies the calculation of the other. This shared approach results result in the publication of an agreed upon product, which eliminates the risk confusing the users of trade statistics.

29.26.    Example of Italy. InItaly, monthly trade time series are seasonally adjusted by means of TRAMO-SEATS (Windows version). In particular, intra- and extra-European Union series (at import and at export) are adjusted directly and separately, while the series referring to total trade (intra- and extra-European Union) at import or at export are obtained indirectly as sums of the corresponding seasonally adjusted series, owing to the well-known aggregation problem. The models selected by TRAMO-SEATS are revised at the beginning of a new year, but the estimated SA coefficients are revised monthly as soon as a new observation is added to the series. While this approach obviously implies the need for some revisions for the nearest time lags, it gives more consistent overall-year information as compared with raw data. The selected models are available to researcher or users on request.

29.27.    Example of the United States of America. Monthly merchandise trade series are seasonally adjusted using factors that are produced once a year during an annual revision cycle.  Factors are produced for each month of the coming 12-month period, and are revised for the previous three years.  The X-13ARIMA-SEATS program is used to analyse data series and generate the seasonal adjustment factors.   Data are aggregated into 269 total import and export five-digit end-use commodity groupings which are examined for trading-day variation and seasonality.  The end-use commodity classification system combines data into broad categories based on principal uses of the commodities; utilization of the system ensures methodological consistency with quarterly adjusted balance-of-payments data.  Seasonal factors are generated for those groups that show significant predictable seasonality.  The factors are used to adjust the data in the most detailed end-use categories.  These detailed adjusted data are then summed to the one-digit end-use level for release with the monthly merchandise trade totals.

29.28.    Example of Norway. In the case of monthly data, the main figures for import and export are adjusted seasonally using X-12-ARIMA, in addition to a number of selected series at the two-digit level of SITC. A few monthly data series at the three-digit level of SITC are also adjusted.  In the case of quarterly data, seasonal adjustments are applied to volume indices on total imports and exports in addition to some selected series as described above in the case of monthly figures.Norway’s External Trade Division is assisted by one or two experts, when needed, who support all fields dealing with seasonal adjustments in Statistics Norway. These experts also participate from time to time in the conduct of a more in-depth evaluation of the methods used.

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