1. On temporal aggregation and seasonal adjustment
Does the order matter?
Anna Ciammola, Claudia Cicconi
Francesca Di Palma
ISTAT - Italy
Workshop on methodological issues in Seasonal Adjustment
Luxembourg, 6 March 2012

2. Outline of the presentation
Statement of the problem
Our experiment
Results
Final remarks

3. Statement of the problem
Sometimes seasonally adjusted data, required at quarterly frequency, can be derived from raw data available at monthly frequency
Two possible approaches for seasonal adjustment (SA)
On monthly data (SA first, quarterly aggregation later)
On quarterly data (quarterly aggregation first, SA later)
The minimization of revisions of SA series can represent a criterion to choose between the two alternatives

4. QNA: the framework
QNA are derived applying temporal disaggregation techniques with related indicators to annual data
Chow-Lin (1971) and, occasionally, Fernandez (1981)
Quarterly unadjusted, working-day adjusted (WDA) and seasonally adjusted (SA) data are derived through three separate disaggregation processes
Unadjusted NA annual data and quarterly short-term indicators  Unadjusted QNA
WDA annual data and quarterly WDA indicators  WDA QNA Monthly indicators: WDA indicators are derived from Tramo at monthly frequency and then quarterly aggregated

5. QNA: the framework
WDA annual data (as in step 2) and quarterly SA indicators  SA QNA Quarterly indicators: SA indicators are derived from Tramo-Seats at quarterly frequency (processing quarterly WDA data)
Major domains where monthly reference indicators are available
Industrial production and foreign trade

6. Aim of the analysis
To investigate whether the order of temporal aggregation (TA) and SA matters in terms of revisions of seasonally adjusted data
Previous analysis
Di Palma and Savio (2000):
Theoretical properties of revisions in the model-based decomposition
Empirical analysis implemented omitting WDA
Our contribution
Considering WDA as part of the analysis
Different indicators on revisions estimated on a longer time span
More general simulation exercise and empirical results on industrial production indicators (IPI)

7. TA of seasonal ARIMA models
Well documented in the literature on time series
Wey (1978), Geweke (1978), …
…, Silvestrini, Veredas (2008)
Quarterly aggregation (QA) of monthly data
Invertible ARIMA  QA  Invertible ARIMA
The order of the autoregressive part of the model (stationary and non-stationary) does not change
The order of the moving average (MA) part of the model may change
The airline model
(0,1,1)(0,1,1)12  QA  (0,1,1)(0,1,1)4
The seasonal MA parameter not affected by QA

8. Our experiment Aim Exercise on simulated series
Analysis of revisions on both SA data in level and q-on-q growth rates (GR), when SA is implemented before and after QA
Exercise on simulated series
Application on the indicators of industrial production

9. Revisions and their measures
For both SA data in levels and GR
The target of the revision analysis is the concurrent estimates (SAt|t or GRt|t)
How concurrent estimates change when 1, 2, 3 or 4 quarters are added (SAt|t+step i or GRt|t+step i)
Revisions computed over a 12 year span (48 iterations)
Measures on revisions of quarterly SA levels and GR
Mean of revisions (MR)
Mean of absolute revisions (MAR)
Root mean squared revisions (RMSR)
Quarterly SA data
Monthly data  QA  SA (hereafter Q  SA)
Monthly data  SA  QA (hereafter M  SA  Q)

10. Simulation exercise (1)
Airline models
25 models with q and Θ = {-.1, -.3, -.5, -.7, -.9}
100 monthly series for each model (22 years)
QA to derive quarterly series
48 iterations for each series, adding one new quarter (three new obs. for monthly data)
Issue: simulation of series on which GR can be computed
Initial conditions in the data generation process different from zero
Transformation of generated time series (with initial conditions = 0) in indices  our choice
Constant
Scale factor

11. Simulation exercise (2)
Tramo-Seats processing
Automatic identification of the ARIMA model
Computation of revisions on quarterly SA data

12. Results on simulated series: quarterly SA data
RMSR MSAQ
RMSR QSA Θ
-0.9
-0.7
-0.5
-0.3
-0.1 q
1 step
0.51
0.64
0.73
0.72
0.92
0.56
0.69
0.82
0.96
0.79
0.89
0.57
0.99
0.63
0.74
1.01
0.60
0.81
0.83
0.85
1.02
4 step
0.80
0.87
0.95
0.97
0.84
0.93
0.62
0.65
0.78
0.98
0.90
0.68
0.86

13. Results on simulated series: q-on-q GRΘ
-0.9
-0.7
-0.5
-0.3
-0.1 q
1 step
0.40
0.38
0.42
0.63
0.80
0.44
0.60
0.83
0.92
0.69
0.86
1.01
0.56
0.62
0.90
0.97
1.10
0.50
0.78
0.93
1.13
4 step
0.54
0.81
0.94
0.98
0.72
0.85
0.95
0.96
0.67
0.82
RMSR MSAQ
RMSR QSA

14. Empirical analysis (1) Industrial production indicators
Total index and 16 industrial sectors
WDA data
Sample: 1990 – 2011
1990q1-2000q1: first estimation sample
48 iterations for each series, adding one new quarter (three new obs. for monthly data)
Partial concurrent approach with some constraints
At the end of the year, current model and identification of outliers in the last 12 (4) obs.
Identification of a new model in case of diagnostics failure, non-significance/instability of parameters

15. Empirical analysis (2)
Current processing
Reg-Arima model fixed and parameter estimation run every quarter
On monthly data
On quarterly data
Computation of revisions on quarterly SA data and growth rates

16. Results on real data: quarterly SA data
RMSR - (SAt|t + step i − SAt|t) / SAt|t
Circle size is proportional to the sectorial weight (the biggest circle represents the total industrial index)

17. Results on real data: q-o-q GR
RMSR - (GRt|t + step i − GRt|t)
Circle size is proportional to the sectorial weight (the biggest circle represents the total industrial index)

18. Final remarks Results from the simulation exercise
M  SA  Q outperforms Q  SA in terms of revisions on both SA data and growth rates, when airline model is considered with negative parameters (true sign)
This result is more clear-cut when
Both regular and seasonal MA parameters are near the non-invertibility region
Time series are not very long (results not reported in this presentation)

19. Final remarks Results from empirical analysis on IPI Further analysis
M  SA  Q slightly outperforms Q  SA in terms of revisions on both SA data and growth rates, supporting evidence from simulation
Further analysis
More ARIMA models for simulations
(1,1,0)(0,1,1)
(2,1,0)(0,1,1)
Different sample lengths
Applications on other domains (e.g. foreign trade)