Seasonal Adjustment in Times of Strong Economic Changes Jens Mehrhoff* Deutsche Bundesbank 6 th Eurostat Colloquium on Modern Tools for Business Cycle Analysis Luxembourg, 26-29 September 2010 *This presentation represents the author’s personal opinions and does not necessarily reflect the *views of the Deutsche Bundesbank or its staff.
1. General principles of seasonal adjustment ❙ Seasonally adjusted data have proven helpful in monitoring the current economic situation, particularly in order to gain information about news and turning points at an early stage. ❙ However, abrupt sharp economic movements, such as the recent financial and economic crisis, also affect the calculation of seasonally adjusted data. ❙ The interplay of fact and diagnosis will be examined in this presentation using data on Argentine currency in circulation. ❙ The different revision policies contained in the ESS Guidelines on Seasonal Adjustment will be used with the X-12-ARIMA and TRAMO/SEATS methods. Luxembourg, Seasonal Adjustment in Times of 2 26-29 September 2010 Strong Economic Changes
1. General principles of seasonal adjustment ❙ According to these guidelines, the purpose of seasonal adjustment is to filter out the usual seasonal fluctuations, i.e. those movements that recur with similar intensity in the same season each year (item 0). ❙ Hence, this implies that unusual movements that are readily understandable in economic terms will continue to be visible. Therefore, it is necessary that these unusual movements are treated as outliers and thus not attributed to seasonal factors (item 1.4). ❙ Given that a crisis does not occur year after year and the persistence of the conditions responsible for seasonality, one could either use appropriate outlier variables or forecast seasonal/calendar factors in these times. Both approaches guarantee that the full effects of the crisis remain visible in seasonally adjusted data (item 3.2). Luxembourg, Seasonal Adjustment in Times of 3 26-29 September 2010 Strong Economic Changes
2. The case of Argentine currency in circulation ❙ The 2008/2009 financial and economic crisis is not long enough ago to allow the evaluation of its final effects on seasonality and seasonal adjustment. For this reason, the empirical example chosen here is that of Argentine currency in circulation, which was affected by the 2001/2002 Argentine crisis. ❙ Three different regimes can be identified in the time series. The first of these is the time before the Argentine crisis, in particular the period from January 1992 to November 2001. The height of the crisis covers the months from December 2001 to May 2002 – this view is supported by the outlier identification of RegARIMA modelling. Finally, from June 2002 to December 2007 a new development of the time series can be observed. Luxembourg, Seasonal Adjustment in Times of 4 26-29 September 2010 Strong Economic Changes
Luxembourg, Seasonal Adjustment in Times of 5 26-29 September 2010 Strong Economic Changes
3. Seasonal adjustment before the crisis ❙ A more detailed inspection of unadjusted data reveals a certain pattern of seasonality in currency in circulation. There are peaks in December/January followed by troughs until July, when the value of currency in circulation peaks again before declining until December. Looking at reasons behind this pattern, it is the extra half-wage payments received in July and December/January which are the prime cause of the seasonality. ❙ As the time series is a monthly stock series of daily averages it shows working day effects. For the sake of parsimony and in order to avoid multicollinearity, two regressors are built. The “Monday” regressor counts the number of Mondays minus the number of Fridays. Tuesdays, Wednesdays and Thursdays are put together in the “weekday” regressor, with their number again being measured in deviation from the number of Fridays. Additionally, a special Christmas regressor is set up which counts the number of working days within 15 calendar days before Christmas. Luxembourg, Seasonal Adjustment in Times of 6 26-29 September 2010 Strong Economic Changes
3. Seasonal adjustment before the crisis ❙ Prior to estimation, unadjusted data are transformed into natural logarithms. In addition to the aforementioned three calendar regressors, the baseline model (as of November 2001) consists of a constant term and a level shift for August 2001. The ARIMA model is seasonally and non-seasonally integrated with both a seasonal and non-seasonal AR term and a seasonal MA term, i.e. ln(1 1 0)(1 1 1) 12 . ❙ Following the Argentine practice, the monthly-specific seasonal smoothing filters in the seasonal adjustment core of X-12-ARIMA, hereinafter referred to as X-12, are set to 3 × 9. By contrast, the decomposition with SEATS is based solely on signal extraction from TRAMO's RegARIMA model. Estimation is performed with an experimental version of the hybrid program X-13ARIMA-SEATS. Luxembourg, Seasonal Adjustment in Times of 7 26-29 September 2010 Strong Economic Changes
3. Seasonal adjustment before the crisis Table 1: Estimated semi-elasticities of the calendar regressors Parameter Standard Variable t -value estimate error “Monday” 0.17 0.091 1.90 regressor “Weekday” –0.04 0.029 –1.52 regressor Christmas 0.30 0.253 1.17 regressor Luxembourg, Seasonal Adjustment in Times of 8 26-29 September 2010 Strong Economic Changes
Luxembourg, Seasonal Adjustment in Times of 9 26-29 September 2010 Strong Economic Changes
4. Seasonal adjustment during the crisis ❙ At the end of 2001, one of the worst political, economic and social crises in Argentina broke out. In order to avoid a bank run, the government de facto froze all bank accounts in December 2001. The most striking feature of currency in circulation is the change in the exchange rate regime beginning in January 2002. At the beginning of 2002, the national government declared that it would halt repayments on its national debt and strongly devalued the peso, adopting a managed float regime. ❙ How should one deal with such a situation in the context of seasonal adjustment? The ESS Guidelines suggest two viable alternatives for seasonally adjusting new data. Either partial concurrent adjustment where the extraordinary effects of the crisis are accounted for by the introduction of outlier variables or the use of forecast seasonal and calendar factors in combination with internal checks, i.e. controlled current adjustment. Luxembourg, Seasonal Adjustment in Times of 10 26-29 September 2010 Strong Economic Changes
4. Seasonal adjustment during the crisis ❙ In what follows, revisions from partial concurrent adjustment are analysed with and without outliers in both RegARIMA modelling and – for X-12 only – the seasonal adjustment (SA) core. The model is identified based on November 2001 data. ❙ Provided RegARIMA outlier variables are introduced into the model, the following will be used which are identified both in real time and ex post (the corresponding t -values are at least about four in absolute terms throughout): ❙ a level shift in December 2001, ❙ an additive outlier in January 2002, ❙ an additive outlier along with a level shift in February 2002 and ❙ a level shift in May 2002. Luxembourg, Seasonal Adjustment in Times of 11 26-29 September 2010 Strong Economic Changes
4. Seasonal adjustment during the crisis ❙ While the model parameters are re-estimated, the model specification is kept constant. ❙ Revisions are calculated with the concurrent estimate as target, i.e. revision = later estimate/first estimate – 1, showing how much a given adjustment changes when adding more data. Old unadjusted data remain unchanged, i.e. revisions are not calculated in real time but much like the automatic History procedure, known from X-12-ARIMA. Luxembourg, Seasonal Adjustment in Times of 12 26-29 September 2010 Strong Economic Changes
Luxembourg, Seasonal Adjustment in Times of 13 26-29 September 2010 Strong Economic Changes
4. Seasonal adjustment during the crisis ❙ When outliers are correctly specified in RegARIMA modelling, the revisions from the X-12 method and the SEATS method are similar, although X-12 produces somewhat lower revisions than SEATS. Conversely, if RegARIMA outliers are neglected, revisions skyrocket. The need for outlier modelling becomes even more obvious when considering SEATS without RegARIMA outliers: the estimated model is of little use, if at all, and thus SEATS fails to estimate the seasonal factor reliably. In some cases, SEATS is unable to admissibly decompose the model and has to replace it with a decomposable one. ❙ As regards revisions, RegARIMA outlier modelling is more important than extreme value detection in X-12's seasonal adjustment core. Nonetheless, employment of seasonal adjustment core outliers lowers revisions, especially if RegARIMA outliers are disregarded. Eventually, there is strong evidence that seasonality is present even in times of crisis. Luxembourg, Seasonal Adjustment in Times of 14 26-29 September 2010 Strong Economic Changes
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