Transcript Monitoring the Economy: an Application of Multivariate

Monitoring the Economy: an
Application of Multivariate RealTime Signal Extraction
http://blog.zhaw.ch/idp/sefblog
http://www.idp.zhaw.ch/usri
http://www.idp.zhaw.ch/MDFA-XT
Pot-Pourri Recent Experiences
• Basic topics
• Real-time multivariate filtering
– What it is and what it isn‘t
• Customized optimization criteria
• Performances (USRI)
• Misspecification and the `financial crisis‘
A Selection of Basic Topics
USRI
MDFA-XT
List of Important Requirements
• A priori knowledge:
– Data selection, constraints
• User requirements: customization
– Minimize Revisions
– Reliability: effective noise elimination
– Timeliness: detecting relevant patterns fast
• Revisions/publication strategy:
– Reveal true historical performance
Requirements
• Consistency
– Classical-, growth- and acceleration cycles
– Various statistics emphasize a common
target/proceeding
• Replicability/transparency:
– algorithm, no human intervention (subjective
judgemental adjustments)
• Real-Time Benchmarking:
– Real-time comparisons
USRI http://www.idp.zhaw.ch/usri
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•
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A priori knowledge: NBER-Design
User requirements: MDFA
Revisions: WYSIWYG-Design
Consistency: Unifying statistical design for
all three cycles
• Replicability: Excel sheet, USRI-site
• Benchmarking:
http://blog.zhaw.ch/idp/sefblog
Real-Time Multivariate
Filtering
What it is
What it isn‘t
Estimation Problem
Data: X t , W1t ,...,Wmt , t  1,..., T

Target: Yt 

 k X t k

k 
Multivariate Real-Time Filter:
T 1
 ˆ
k 0
0k
T 1
T 1
k 0
k 0
X T  k   ˆ1kW1,T  k  ...   ˆmkWm ,T k
Objective: choose ˆik such that some prespecified requirements
are met
Pseudo-Multivariate Filtering
• Direct vs. Indirect Filtering:
– aggregate data prior to univariate filtering or
(univariate) filtering prior to aggregation?
– Direct: filtering the output of a dynamic factor
model
• Linear univariate (HP, CF, X-12-ARIMA)
• Non-linear univariate: MS-model
– Indirect: Seasonal adjustment
• It was/is impossible to find unadjusted USmacrodata for USRI
• Inconsistency
Objectives
• Statistical agency: minimize revisions
• Forecasting institute/fund manager/trader: detect
turning-points
• Neither problem is related directly to one-step
ahead mean-square optimization
– So why should we rely on maximum likelihood?
Customized Optimization
Criteria
1. Revisions Univariate
2
T
(T 1) / 2

k  (T 1) / 2
| (k )  (k ) | ITX (k )  Min
2
• Minimize a (uniformly) superconsistent
estimate of an (uniformly) efficient
estimate of the filter mean-square error
• (Customized) Efficiency enters explicitly in
the Design of the Optimization Criterion
2. Operationalizing Fuzzy
`Timeliness‘
[T / 2]
 2
ˆ ( ) |2 I ( )
|

(

)

A
k
k
NX
k

 T  k 0
min ˆ 
 2 [T / 2] 2 A( ) Aˆ ( )(1  cos(
ˆ ( )))I ( )
k
k
k
NX
k
k 0


T
•λ>1: emphasize the time delay in the pass-band
•λ=1: best level filter
3. Operationalizing Timeliness and
Reliability
 2 [T / 2]
2
ˆ ( ) |2 I ( )
W
(

)
|

(

)

A
k
k
k
NX
k
 T  k 0
min ˆ 
 2  [T / 2] 2W ( ) 2 A( ) Aˆ ( )(1  cos(
ˆ ( )))I ( )
k
k
k
k
NX
k
k 0

T
• Stronger damping of highfrequency noise in stop-band
• Smaller time delays in pass-band
• W(ω) is monotonic (increasing)
and λ>1
W ( )

4. Multivariate: Revisions
Cointegration (Rank=1)
2
T
(T 1) / 2

k  (T 1) / 2
| Tr '(k ) |2

Min

 (0)  exp(ik )(k )

Tr '(k )  (0)TC (k )  exp(ik ) 
 (0)  T X (k ) 
1  exp(ik )



 (0)  exp(ik )(k )

 (0)  T X (k ) 

1  exp(ik )


 ˆ h (0)  exp(ik )ˆ h (k )

  h (0)  T Wh (k )


1  exp(ik )
h 1 

m
5. Multivariate
Turning-Points
• Insufficient space…
Upshot
• There are meaningful alternatives to the
ubiquitous `one-step ahead‘ paradigm.
Performances
Look-Back
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2005/2006: KOF-economic barometer, Dainties
2007/2008: Forecasting competitions
2008: Health-care forecasts
2008: Output-gap US- and Euro-GDP
March 2009: USRI
– CIRET-conference Sept 2008
– MDFA Fall 2008
• Oct. 2009: MDFA-XT
• 2010: EURI, competition
• Collected evidences for systematic
outperformance in various application fields
Performances USRI
• On-line since March 2009
• http://blog.zhaw.ch/idp/sefblog
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–
–
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CFNAI
OECD-CLI
LEI and CEI
ADS
MS-designs: Chauvet, Piger
• Troughs of acceleration-, classical- and growthcycles as early as December 2008, April 2009
and June 2009 without subsequent revisions
MDFA-B and MDFA-E
Classical and Acceleration Cycles
USRI and Fundamental Trading
Financial Trading
Google for “MDFA-XT”
First guess
MDFA-XT Unfrequent
MDFA-XT (Unfrequent to Mid)
MDFA-XT Mid
MDFA-XT Mid to Frequent
MDFA-Frequent
Model Misspecification
OECD-CLI
http://blog.zhaw.ch/idp/sefblog/index.php?/archives/35Did-you-say-a-negative-trend-growth-How-traditionalbandpass-filters-distort-underestimate-and-shift-thelatest-2008-recession!.html
10 Year HP-filter
GARCH(1,1) Log-Returns IPI
Reconstructed HP-Compatible IPI
Remove Variance Effect, Retain
mean-Effect
Conclusion
Public Exposition
• Welcome (positive) pressure for lazy
minds
• Public exposition `pusher’
– Careful prototypical setting
– Mental presence
• Frequent performance check
• Discussions with users
• Ideas for improvements
Links
• http://blog.zhaw.ch/idp/sefblog
• http://www.idp.zhaw.ch/usri
• http://www.idp.zhaw.ch/MDFA-XT