1

Anna Ciammola, Claudia Cicconi

Francesca Di Palma

ISTAT - Italy

Workshop on methodological issues in Seasonal Adjustment

Luxembourg, 6 March 2012

Does the order matter?

On temporal aggregation and seasonal adjustment

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Outline of the presentation

Statement of the problemOur experimentResultsFinal 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)1.On monthly data (SA first, quarterly aggregation later)

2.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 dataChow-Lin (1971) and, occasionally, Fernandez (1981)

Quarterly unadjusted, working-day adjusted (WDA) and seasonally adjusted (SA) data are derived through three separate disaggregation processes1.Unadjusted NA annual data and quarterly short-term

indicators Unadjusted QNA2.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

3. 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

decompositionEmpirical analysis implemented omitting WDA

Our contributionConsidering WDA as part of the analysisDifferent indicators on revisions estimated on a longer time

spanMore 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 ARIMAThe order of the autoregressive part of the model (stationary

and non-stationary) does not changeThe 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 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 seriesApplication on the indicators of industrial

production

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Revisions and their measures Revisions

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)

1. Airline models 25 models with 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)

2. 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)

3. 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

      Θ

      -0.9 -0.7 -0.5 -0.3 -0.1

1 step

-0.9 0.51 0.64 0.73 0.72 0.92

-0.7 0.56 0.69 0.82 0.92 0.96

-0.5 0.72 0.79 0.89 0.57 0.99

-0.3 0.63 0.74 0.96 0.92 1.01

-0.1 0.60 0.81 0.83 0.85 1.02

4 step

-0.9 0.60 0.80 0.87 0.81 0.95

-0.7 0.63 0.80 0.87 0.95 0.97

-0.5 0.73 0.84 0.93 0.62 0.99

-0.3 0.65 0.78 0.98 0.90 0.96

-0.1 0.68 0.84 0.86 0.87 0.95

RMSR MSAQ

RMSR QSA

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Results on simulated series: q-on-q GR

RMSR MSAQ

RMSR QSA

      Θ

      -0.9 -0.7 -0.5 -0.3 -0.1

1 step

-0.9 0.40 0.38 0.42 0.63 0.80

-0.7 0.44 0.44 0.60 0.83 0.92

-0.5 0.60 0.69 0.86 0.92 1.01

-0.3 0.56 0.62 0.90 0.97 1.10

-0.1 0.50 0.78 0.80 0.93 1.13

4 step

-0.9 0.54 0.81 0.93 0.94 0.94

-0.7 0.62 0.81 0.90 0.98 0.94

-0.5 0.72 0.85 0.95 0.95 0.96

-0.3 0.67 0.82 0.96 0.92 0.92

-0.1 0.67 0.86 0.86 0.93 0.90

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Empirical analysis (1)

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)

2. 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)

3. Current processing

Reg-Arima model fixed and parameter estimation run every quarter On monthly data On quarterly data

4. Computation of revisions on quarterly SA data and growth rates

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Results on real data: quarterly SA data

0 0.5 1 1.5 2 2.50

0.5

1

1.5

2

2.5One-step

Q-->SA

M--

>S

A--

>Q

0 0.5 1 1.5 2 2.50

0.5

1

1.5

2

2.5Two-step

Q-->SA

M--

>S

A--

>Q

0 0.5 1 1.5 2 2.50

0.5

1

1.5

2

2.5Three-step

Q-->SA

M--

>S

A--

>Q

0 0.5 1 1.5 2 2.50

0.5

1

1.5

2

2.5Four-step

Q-->SA

M--

>S

A--

>Q

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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0 1 2 3 40

1

2

3

4One-step

Q-->SA

M--

>S

A--

>Q

0 1 2 3 40

1

2

3

4Two-step

Q-->SA

M--

>S

A--

>Q

0 1 2 3 40

1

2

3

4Three-step

Q-->SA

M--

>S

A--

>Q

0 1 2 3 40

1

2

3

4Four-step

Q-->SA

M--

>S

A--

>Q

Results on real data: q-o-q GRRMSR - (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 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)