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The KOF Economic Barometer: anApplication of Customized Criteria

SSS 2006SSS 2006LuganoLugano

MarcMarc WildiWildiInstitute of Data Analysis and Process DesignInstitute of Data Analysis and Process Design

www.idp.zhwin.chwww.idp.zhwin.chwia@zhwin.chwia@zhwin.ch

www.idp.zhwin.ch

Introduction

FrameworkFrameworkStatisticalStatistical problemproblem

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Framework: revision of the KOF economicbarometer

New KOF-economic barometer launched in April2006

Extended data set (KOF):

New filter technique (DFA)

Concurrent (real-time) filter-output published only

Trend

No revisions

Statistical Problems

1. Fast and reliable detection of Turning Points

2. Minimization filter error variance (level-filter)

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GDP and old KOF-economic barometerEx Post

Bisheriges KOF-Barometer

Standardized Growthrates

-3

-2

-1

0

1

2

3

84 86 88 90 92 94 96 98 00 02 04

-3

-2

-1

0

1

2

3

GDP

KOF-Barometer

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KOF-economic barometer in real time

-1.5

0

1.5

2001 2002 2003

Direkter Filteransatz

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Ex Post vs. Real Time

Ex-post:

The old indicator leads by a few months (1-3)

In real time:

Filter delay of X-11 is ~2 months

Unreliability adds ~2 months

Indicator lags

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Part IReal-Time Level Approximation

CriterionCriterion::MeanMean--SquareSquare ErrorError

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Filters

Symmetric filters:

Advantages:

Vanishing time delay: input and output signalsare synchronized

Strong damping of noise: smoothness/reliability

Diasadvantage

Cannot be used towards sample end-point– Future observations are missing

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Methodological approachesReal-time (concurrent) filters

Model Based Approach (TRAMO/X-12-ARIMA)

Identify a time series model for the DGP

Forecast the future (one- and multi-step forecasts)

Apply the symmetric filter to the extended timeseries

Direct Filter Approach, DFA (Wildi,2004)

Minimize an efficient estimate of the filter errorvariance

Efficiency!

Introduction

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DFA-Criterion

/ 22 2

1

/ 22

1

( ( ) ( )) ( ) ( )

*2* ( ) ( )(1 cos( ( ))) ( ) ( )

N

k k k NX kk

N

k k k k NX kk

A A W I

A A W I

•Level Filter•λ=1•W=1

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Empirical ResultsReal-Time Estimates

DFA vs.DFA vs.TRAMO/SEATSTRAMO/SEATS

XX--1212--ARIMAARIMA

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Data

36 (business survey) and 63 (FED diffusion indices)monthly time series

Bounded series (Unit roots are misspecifications)

Rich and complex dynamic structure

Samples of length 60 and 120.

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Performance DFA vs. MBA :Business survey (36 series), Ideal Trend

out of sample out of sample out of sample

120 Observations median 68% 67% 77%

60 Observations median 62% 64% 55%

TRAMO X-12-T X-12-A

Criterion: MSE(DFA)/MSE(MBA)

Boundary filter: performance measure

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Performance DFA vs. MBA :Diffusion Indices (63 series, 60 Obs.), Ideal Trend

60 Obs.

Median Median Median

out of sample (1 year) 48% 48% 67%

out of sample (2 years) 51% 50% 74%

TRAMO X-12-T X-12-A

Boundary filter: performance measure

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Inefficiency of MBA

MethodologicalMethodological issuesissues

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TRAMO: heavy misspecification (120 Obs.)

Series nmb. Models d Series nmb. Models d

1 (210)(011) 2 19 (100)(011) 1

2 (011)(011) 2 20 (011)(011) 2

3 (011)(011) 2 21 (011)(011) 2

4 (011)(000) 1 22 (011)(000) 1

5 (210)(100) 1 23 (100)(000) 0

6 (110)(000) 1 24 (010)(001) 1

7 (100)(011) 1 25 (011)(011) 2

8 (011)(011) 2 26 (013)(001) 1

9 (011)(011) 2 27 (011)(011) 2

10 (121)(011) 3 28 (110)(000) 1

11 (110)(011) 2 29 (011)(011) 2

12 (011)(000) 1 30 (012)(000) 1

13 (300)(011) 1 31 (011)(011) 2

14 (011)(001) 1 32 (011)(000) 1

15 (011)(011) 2 33 (010)(011) 2

16 (110)(000) 1 34 (010)(011) 2

17 (011)(011) 2 35 (011)(011) 2

18 (011)(011) 2 36 (112)(000) 1

•Business survey data: bounded time series

Introduction

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Series 31: Model, series and simulation (300Obs.)

12 12(1 )(1 ) (1 0.6622 )(1 0.8238 )t tB B X B B

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How useful are model diagnostics?

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Problem MBA: one-step ahead perspective

Statistics based on one-step ahead forecasts

Estimation, Identification (AIC/BIC, unit-rootstests,…), Diagnostics (Box-Pierce, Ljung-Box)

Cannot detect Misspecification

Conflict one vs. multi-step ahead forecasts

Consequences

Inefficient concurrent filters

Unnecessarily large time delays

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Summary Level Approximation

Model-based approaches perform

`well´ with respect to one-step ahead forecasting

`bad´ with respect to multi-step ahead performances

`bad´ with respect to real time signal extraction

Severe model misspecification

Optimization criterion (statistics) does not mate therelevant estimation problem

Turning points cannot be accounted for explicitly

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PART II

Detection of Turning PointsDetection of Turning Points

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Leakage Problem in the vicinity of TP’s

TP-detectionandlevel estimation: twoincongruent criteria

2003M11 2004M2 2004M5 2004M8 2004M11 2005M3

0.0

0.2

0.4

0.6

0.8

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Problem

Level approximation and detection of TP’s areincongruent criteria

Leakage

Noise becomes visible in vicinity of TP’s becausetrend is flat.

Time delay is often too large

More general criterion is needed

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DFA-TP-Criterion

/ 22 2

1

/ 22

1

( ( ) ( )) ( ) ( )

*2* ( ) ( )(1 cos( ( ))) ( ) ( )

N

k k k NX kk

N

k k k k NX kk

A A W I

A A W I

•TP-Filter•λ>1: Speed•W(ω)= ω2: Reliability

•Speed and Reliability at costs of level.

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Filter characteristics KOF-Barometer:Amplitude DFA TP-filter vs. DFA level filter

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Filter characteristics:Delay TP-filter vs. level filter

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Characteristics DFA-TP Filter

Fast

Vanishing time delay

Reliable

Extremely smooth (real-time filter)

No more noise towards TP‘s

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TP-filter vs. Level Filter

-2

-1

0

1

2

3

4

1994

1994

1995

1995

1996

1997

1997

1998

1998

1999

1999

2000

2001

2001

2002

2002

2003

2004

2004

2005

Barounfiltered

LevelFilter

TP-Filter

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TP-Filter vs. Logit-Model

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Performance TP-filter vs. Logit

Logit TP

Total false alarms 12% 11%

Delays 7% 4%

Anticipations 2.50% 7%

RandomAlarms 2.50% 0%

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Economic Sentiment Indicator (ESI) for theeuro area, published monthly by DG ECFIN.

DFADFA vsvs DaintiesDainties

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Dainties

No revisions

Seasonal adjustment procedure

Study by Franses,Paap, Fok (2005) :

For the ESI Dainties performs well in comparison toTRAMO/SEATS or Census X-12-ARIMA

Seasonal components are weak (`deterministic´)

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In the past (DFA: fast and reliable)

90.000000000

95.000000000

100.000000000

105.000000000

110.000000000

115.000000000

Apr96

Jul96

Okt96

Jan

97

Apr97

Jul97

Okt97

Jan

98

Apr98

Jul98

Okt98

Jan

99

Apr99

Jul99

Okt99

Jan

00

Apr00

Jul00

Okt00

Jan

01

Apr01

Jul01

DFA

Dainties

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Towards the current boundary

92.000000000

94.000000000

96.000000000

98.000000000

100.000000000

102.000000000

104.000000000

106.000000000

Aug03

Okt

03

Dez03

Feb04

Apr 0

4

Jun04

Aug04

Okt

04

Dez04

Feb05

Apr 0

5

Jun05

Aug05

Okt

05

Dez05

Feb06

Apr 0

6

DFA

Dainties

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Amplitude and Time delay DFA

-1.00E+00

0.00E+00

1.00E+00

2.00E+00

3.00E+00

4.00E+00

5.00E+00

6.00E+00

7.00E+00

0

π/6

2π

/6

3π

/6

4π

/6

5π

/6 π

0.00E+00

5.00E-01

1.00E+00

1.50E+00

2.00E+00

2.50E+00

Delay

Amplitude

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Improving Leading Indicators in RealTime!

ThankThank youyou forfor youryourattentionattention

Contact:wia@zhwin.chContact:wia@zhwin.ch

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Supplement:Methodological Shift in Real Time

Signalextraction

FilterFilter errorerror diagnosticsdiagnostics

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Series 4 Business Survey: Ideal Trend

(1 ) (1 0.2063)t tB X

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Filter Diagnostics

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Filter (revision) Error Diagnostics

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Conclusions

Diagnostics are based on

Filter characteristics (amplitude, time delay)

Filter errors: `suspect´ spectral peaks

Directly related to real time signalextraction