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**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

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**Outline of the presentation**

Statement of the problem Our experiment Results Final remarks

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**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

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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

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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

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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)

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**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

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**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

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**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)

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**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

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**Simulation exercise (2)**

Tramo-Seats processing Automatic identification of the ARIMA model Computation of revisions on quarterly SA data

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**Results on simulated series: quarterly SA data**

RMSR MSAQ RMSR QSA 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

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**Results on simulated series: q-on-q GR**

Θ -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 MSAQ RMSR QSA

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**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

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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

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**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)

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**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)

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**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)

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**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)

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