Recession Impact

(If you are not familiar with the Camplet procedure, first read “Camplet in a nutshell”.)
One pleasant aspect of the 2008/2009 recession is, that it renders time series with sudden and strong direction changes of the trend/cycle and it can be checked how analysis procedures deal with these: is there a time lag between the actual change in direction and the outcomes of seasonal adjustment? And are there after-effects in the seasonal components in the periods following the recession? In figure 1 the GDP of the Netherlands is depicted for a number of years including the recession years.
Figure 1, GDP of the Netherlands (Eu millions)

The recession began in 2008.4 with a steep drop, to last three quarters before it levelled out. How does the Camplet procedure react? The first indication of change is in the error (e) of extrapolation to 2008.4. Although there had already been a slowdown of the trend in the preceding quarters, the turning point came in 2008.4, with a %e of -2.3%, followed by -3.6% in 2009.1 and then a quarter of
+1% . Note that these percentages are trend changes, not trends: the +1% in 2009.2 means that the trend is still downwards, but at a lesser pace. For a GDP such percentage changes are quite high, however they stay within Camplet’s default LE parameter of 6% and therefore the common adjustment period of 6 quarters is applied to change the NS component (the g-line gradient) by e/6.
When the CA adjustment period is applied there is no time lag:
At every addition of an observation the stretch of time that the NS is calculated over shifts forward by one period. This aspect is comparable to a moving average (MA), but there is one important difference: The MA changes by MAt+1 = MAt + (Yt+1 – Yt+1-Z)/z, where z is the length of the MA. The NS changes by NSt+1 = NSt + s.a.(Yt+1 – Yt)/L, where L is the adjustment period. If a turning point, say downwards, occurs in period Yt+1 , a MA continues to rise while the actual series decreases, as long as Yt+1 > Yt+1-Z . This is the cause of a time lag in updating the SC. Also, after the recession period, the inverse development will at first delay the resetting of the SC, thus creating an echo of the recession in the following periods. In the Camplet procedure, updating NS and SC by the current development (Yt+1 – Yt), there is no cause for time lag or echo.
Recession impact on volatile series.
It was argued that there is no time lag or echo when the fluctuations in a time series remain within the percentage set by LE in its default of 6%. Next the effect in more volatile series will be contemplated. For a good comparison a volatile series will be constructed with similar deviations as in the GDP series, but on a larger scale. To this end the same GDP series, with an average level of some 155.000 (million Euros) per quarter will be reduced in scale by subtracting 140.000 from each quarter value. The quarterly fluctuations will remain the same, but as percentages from the average level they will be much higher. In figures 2a and 2b the outcomes of GDP and reduced GDP are compared.

Camplet is not a black box: for each observation the %e, the setting of all parameters and the adjustment period are quoted in a separate sheet for each series. From these data it can be seen whether there is a time lag in adjusting the reduced version of GDP, and why the first upturn after the recession, in 2009.3, has more impact on the reduced GDP graph. An abstract of these data is given in table 1.

Columns e/L quote the outcomes of e divided by the adjustment period, this is the nominal change of the NS component, the change of gradient of the g-line. The SC t+1,i changes by 1.5 e/L and the SA is Yt+1 – SCt+1,i.
Successive Outliers.
For quarters 2009.1 and 2009.2 the CA adjustment period of 6 was selected, in spite of the fact that the %e (27.4% and 7.7%) are above LE. If an outlier is directly preceded by an outlier in the same direction, Camplet detects a change in the trend and selects the CA adjustment period to adopt at once the new gradient of the g-line.
Does the first outlier create a time lag in the seasonal adjustment? Quarter 2008.4 of the Reduced GDP, when the downturn set in with a 15.6% extrapolation error, is treated as an outlier and limits the impact on the seasonal component. As a result the SA follows the change in the unadjusted series more closely than when the SC were updated simultaneously. So no time lag.
The same can be seen in 2009.3 of the Reduced GDP series, where the adjustment period is raised to 15.4 quarters and the SA follows the rise in the unadjusted series. In the next quarter the SC is updated and reduces the increment of the SA.