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Forecasting the EMU Inflation RateForecasting the EMU Inflation Rate
Linear EconometricsVersus
Non-Linear Computational Models
The 2003 International Conference on Artificial Intelligence, Las Vegas, USAApplications of AI in Finance & Economics
Stefan Kooths, Timo Mitze, Eric Ringhut
Muenster Institute for Computational Economics
University of Muenster/Germany
2
MICEMICE
Forecasting the EMU Inflation Rate
University of MuensterGermany
Outline
• Introduction
• Economics and Econometrics
• Computational Approach (GENEFER)
• Competition Setup
• Competition Results
• Conclusion
Introduction
Economics and Econometrics
ComputationalApproach
CompetitionSetup
CompetitionResults
Conclusion
3
MICEMICE
Forecasting the EMU Inflation Rate
University of MuensterGermany
Introduction
• Inflation Forecasts highly important for economic and political agents
time-lag problem especially for inflation-targeting regimes
• Traditional Approaches (Econometrics) VAR
structural models
reduced form models
• Focus of this paper fully interpretable, non-linear genetic-neural fuzzy
rule-bases (GENEFER)
based on previous work (1-quarter-ahead forecasts)
forecasting EMU inflation 1-year-ahead
here:unrestricted VAR
single equation model
Introduction
Economics and Econometrics
ComputationalApproach
CompetitionSetup
CompetitionResults
Conclusion
4
MICEMICE
Forecasting the EMU Inflation Rate
University of MuensterGermany
Long Term Inflation Pressure Measures
• Real Activity Models
output gap (Phillips curve)ygap = y – y*y*: (i) trend, (ii), HP-filter, (iii) Cobb-Douglas PF
mark-up pricingmarkup = p – plr plr = β1 + β2ulclr + β3pimlr
• Monetary Models
real money gap (price gap)mgap = (m-p) – (m-p)*(m-p)* = β1 + β2y* + β3r*
monetary overhang (P-star)monov = (m-p) – (m-p)lr (m-p)lr = β1 + β2y + β3r
Introduction
Economics and Econometrics
ComputationalApproach
CompetitionSetup
CompetitionResults
Conclusion
5
MICEMICE
Forecasting the EMU Inflation Rate
University of MuensterGermany
Expectations and Short Term Disturbances
• Expectational Component
E() = (1-) obj + (obj-1 - -1)
obj: implicit ECB inflation objective
• Short term disturbances (z)
real exhange rate (e)
uncovered interest parity (UIP)
energy price index change (denergy)
oil price change (doil)
seasonal dummies (D)
Introduction
Economics and Econometrics
ComputationalApproach
CompetitionSetup
CompetitionResults
Conclusion
6
MICEMICE
Forecasting the EMU Inflation Rate
University of MuensterGermany
Econometric Modelling
• Step 1:long run relationships via conintegration analysis(dynamic single-equation ARDL approach)
• Step 2:ordinary least squares using error-correction terms from step 1
= D + E() + ecm + z +
Introduction
Economics and Econometrics
ComputationalApproach
CompetitionSetup
CompetitionResults
Conclusion
7
MICEMICE
Forecasting the EMU Inflation Rate
University of MuensterGermany
Data Set
quarterly basis: 1980.1 – 2000.4 (80 observations)
training subset: 1982.2 – 1996.4 (59 observations)
evaluation subset: 1997.1 – 2000.4 (16 observations)
aggregated data for an area-wide model of the EMU based on EU11 (ECB-study)
forecast: quartet-to-quarter change of an artificially constructed harmonized consumer price index (fixed weights for each country)
doil: spot market oil price changes (World Market Monitor)
de: ECU/US$ exchange rate change (Eurostat via Datastream)
EMU implicit inflation target derived from Bundesbank‘s inflation objective (BIS study)
Introduction
Economics and Econometrics
ComputationalApproach
CompetitionSetup
CompetitionResults
Conclusion
8
MICEMICE
Forecasting the EMU Inflation Rate
University of MuensterGermany
Econometric Models: In-sample-fit
Model VariablesR2
(SEE)*
ygap_trend D, ygap_trend(t–1), E(π), de(t–1), doil(t)0,8864
(0,0075)
ygap_hp D, ygap_hp(t–1), E(π), de(t–1), doil(t)0,8674
(0,0081)
ygap_cd D, ygap_cd(t–1), E(π), de(t–1), doil(t)0,8674
(0,0081)
monov D, monov(t–1), E(π), de(t–1), doil(t)0,8654
(0,0083)
markup D, markup(t–1), E(π), de(t–1), doil(t)0,8993
(0,0067)
mgap D, mgap(t–1), E(π), de(t–1), doil(t)0,8433
(0,0078)
eclecticD, ygap_trend(t–1), mgap(t–1), E(π), markup(t–1), monov(t–1), UIP(t–1), denergy(t–2), de(t–1), doil(t), doil(t–2)
0,9425(0,0053)
* Standard Error of Regression
Introduction
Economics and Econometrics
ComputationalApproach
CompetitionSetup
CompetitionResults
Conclusion
9
MICEMICE
Forecasting the EMU Inflation Rate
University of MuensterGermany
Modelling Expectations in Economics (with and without GENEFER)
complete
very high
verylow
none knowledge
abilityto learn
autoregressiveexpectations
rationalexpectations
limit of information processing
boun
dary
to k
now
ledge
adaptivefuzzy rule-based
expectations
Introduction
Economics and Econometrics
ComputationalApproach
CompetitionSetup
CompetitionResults
Conclusion
10
MICEMICE
Forecasting the EMU Inflation Rate
University of MuensterGermany
Adaptive Fuzzy Rule-Based Approach
In a world …
of high complexity
and a high degree of uncertainty
where humans form mental models
we need a modelling approach that …
explicitly represents knowledge (interpretability)
accounts for the uncertainty/vagueness of perceived information and their relations (bounded rationality)
allows for new experiences (learning)
adaptive fuzzy rule-based approach
Introduction
Economics and Econometrics
ComputationalApproach
CompetitionSetup
CompetitionResults
Conclusion
11
MICEMICE
Forecasting the EMU Inflation Rate
University of MuensterGermany
Linguistic Rules and Fuzzification
IF the monetary overhang is medium AND expected inflation is very high THEN future
inflation is high.
monov
1
0
3.8
0.6
4.52.0
0.2
medium highlow
Introduction
Economics and Econometrics
ComputationalApproach
CompetitionSetup
CompetitionResults
Conclusion
12
MICEMICE
Forecasting the EMU Inflation Rate
University of MuensterGermany
Aggregation
IF the monetary overhang is medium AND expected inflation is very high THEN future
inflation is high.
(monetary overhang is medium) = 0.6
(expected inflation is very high) = 0.4
(antecedent) = 0.4 [minimum AND]
(antecedent) = 0.32 [product AND]
Introduction
Economics and Econometrics
ComputationalApproach
CompetitionSetup
CompetitionResults
Conclusion
13
MICEMICE
Forecasting the EMU Inflation Rate
University of MuensterGermany
Inference and Defuzzification
IF the monetary overhang is medium AND expected inflation is very high THEN future
inflation is high.
future inflation
1
0
verylow low medium high
veryhigh
0.4
Introduction
Economics and Econometrics
ComputationalApproach
CompetitionSetup
CompetitionResults
Conclusion
14
MICEMICE
Forecasting the EMU Inflation Rate
University of MuensterGermany
Accumulation
IF... AND...THEN...IF... AND...THEN...IF... AND...THEN...IF... AND...THEN...IF... AND...THEN...IF... AND...THEN...IF... AND...THEN...IF... AND...THEN...IF... AND...THEN...IF... AND...THEN...
Output
IF... AND...THEN...IF... AND...THEN...IF... AND...THEN...IF... AND...THEN...IF... AND...THEN...IF... AND...THEN...IF... AND...THEN...IF... AND...THEN...IF... AND...THEN...IF... AND...THEN...
Introduction
Economics and Econometrics
ComputationalApproach
CompetitionSetup
CompetitionResults
Conclusion
15
MICEMICE
Forecasting the EMU Inflation Rate
University of MuensterGermany
Fuzzy Inference Result Set and Defuzzification
future inflation
1
0
verylow low medium high
veryhigh
4.6 %
Introduction
Economics and Econometrics
ComputationalApproach
CompetitionSetup
CompetitionResults
Conclusion
16
MICEMICE
Forecasting the EMU Inflation Rate
University of MuensterGermany
Knowledge Base
Input1
mediumlow high
Input2
high very highmediumlowvery low
mediumlow high
Output
Rule-Base Fuzzification-Base Weight-Vector
Knowledge-Base = Fuzzy-Rule-Base (FRB)
Weight IF Input1 AND Input2 THEN Output
1 low medium medium
2 low very high high
3 medium very low low
4 high very high high
5 low low low
6 high medium medium
7 high very low medium
8 medium low low
9 medium medium medium
10 high medium medium
Introduction
Economics and Econometrics
ComputationalApproach
CompetitionSetup
CompetitionResults
Conclusion
17
MICEMICE
Forecasting the EMU Inflation Rate
University of MuensterGermany
FRB Learning: What?
(1) adapt fuzzy set widths and centers
w1 IF AND THEN
w2 IF AND THEN
w3 IF AND THEN
w4 IF AND THEN
w5 IF AND THEN
w6 IF AND THEN
w7 IF AND THEN
(1)(2)
(3)
(2) reinforce (forget) used (unused) rules
(3) search for (new) rules
Introduction
Economics and Econometrics
ComputationalApproach
CompetitionSetup
CompetitionResults
Conclusion
18
MICEMICE
Forecasting the EMU Inflation Rate
University of MuensterGermany
Technology Mix for FRB Learning
Input1
mediumlow high
Input2
high very highmediumlowvery low
mediumlow high
Output
Rule-Base Fuzzification-Base Weight-Vector
Knowledge-Base = Fuzzy-Rule-Base (FRB)
Weight IF Input1 AND Input2 THEN Output
1 low medium medium
2 low very high high
3 medium very low low
4 high very high high
5 low low low
6 high medium medium
7 high very low medium
8 medium low low
9 medium medium medium
10 high medium medium
Fuzzy Systems Genetic AlgorithmsArtificial Neural Networks
1 0 10 1 0011 1 1
1 11 00 00 11 1 1
011
1 0 10
1 0
1 10 11
1 00 0
1 1
1 1offspring
parents
create and modify create and modify
GENEFER=
Genetic Neural Fuzzy Explorer
Introduction
Economics and Econometrics
ComputationalApproach
CompetitionSetup
CompetitionResults
Conclusion
19
MICEMICE
Forecasting the EMU Inflation Rate
University of MuensterGermany
Forecasting Steps in GENEFER
• Identify inputs
• Fuzzify all variables
• Generate and tune the rule base
• Infer and defuzzify results
• View and evaluate results, learn from errors
FilteringPerceivedreality
Weight IF Input1 AND Input2 THEN Output
1 low medium medium
2 low very high high
3 medium very low low
4 high very high high
5 low low low
6 high medium medium
7 high very low medium
8 medium low low
9 medium medium medium
10 high medium medium
crisp fuzzy-rule-base
output
Direction of information processing
linguistic levelnumeric level numeric level
Introduction
Economics and Econometrics
ComputationalApproach
CompetitionSetup
CompetitionResults
Conclusion
20
MICEMICE
Forecasting the EMU Inflation Rate
University of MuensterGermany
Competition Setup
• 4-steps-ahead forecast
• 19 Competitors
7 econometric
11 computational
1 benchmark (AR(1))
• Classification
modelling technique
inflation indicator
InflationIndicators
2A
1B
ForecastEvaluation
3ModellingTechnique
A: Real ActivityB: Monetary Activity
1: Econometric2: Computational3: Co-operation
InflationIndicators
2A
1B
ForecastEvaluation
3ModellingTechnique
A: Real ActivityB: Monetary Activity
1: Econometric2: Computational3: Co-operation
Introduction
Economics and Econometrics
ComputationalApproach
CompetitionSetup
CompetitionResults
Conclusion
21
MICEMICE
Forecasting the EMU Inflation Rate
University of MuensterGermany
Competition Criteria (Test Statistics)
• Parametric
mean squared error (MSE)
root mean squared error (RMSE)
mean absolute percentage error (MAPE)
Theil‘s U with an AR(1)
relative mean absolute error (Rel. MAE)
ΔTheil‘s U
• Non-Parametric
confusion rate (CR)
Chi-squared test for independence of 22 confusion matrix (Yates corrected)
Introduction
Economics and Econometrics
ComputationalApproach
CompetitionSetup
CompetitionResults
Conclusion
22
MICEMICE
Forecasting the EMU Inflation Rate
University of MuensterGermany
Competition Results (Overview)
Model MSE RMSE MAPERel. MAE
Theil’s UTheil’s
UCR 2 (1)
2 Yates
AR(1) 1,604 1,267 1,312 1 1 0,974 0,5 0 0,333
ygap_trend 1,074 1,037 0,984 1,005 0,818 0,938 0,417 0,343 0,000
ygap_hp 2,135 1,461 1,446 1,493 1,154 1,311 0,417 0,343 0,000
ygap_cd 2,020 1,421 1,383 1,445 1,122 1,277 0,417 0,343 0,000
monov 0,771 0,878 0,699 0,848 0,693 0,816 0,417 0,343 0,375
markup 1,034 1,017 0,742 0,878 0,803 0,970 0,417 0,343 0,000
mgap 0,569 0,754 0,521 0,692 0,595 0,710 0,500 0,343 0,333
eclectic 1,099 1,048 0,679 0,923 0,828 0,993 0,417 0,343 0,000
g_ygaptrend 1,372 1,171 1,420 1,099 0,925 1,089 0,417 0,343 0,000
g_ygaphp 1,852 1,361 1,075 1,849 1,136 1,174 0,334 1,334 0,333
g_ygapcd 2,233 1,493 1,180 2,000 1,226 1,349 0,167 5,333** 3,000***
g_monov 1,269 1,127 0,976 1,015 0,890 0,884 0,250 3,086*** 1,371
g_markup 1,166 1,080 1,338 0,988 0,853 0,983 0,250 3,086*** 1,371
g_mgap 0,531 0,729 0,794 0,675 0,575 0,629 0,167 5,333** 3,000***
g_eclectic 1,114 1,055 0,822 0,968 0,833 0,999 0,667 1,333 0,333
g_eclectic_ 0,854 0,924 1,001 0,841 0,730 0,806 0,333 1,500 0,375
g_markup_ 0,923 0,961 0,945 0,911 0,759 0,905 0,583 0,343 0,000
g_mgap_ 0,921 0,960 1,083 0,854 0,758 0,862 0,250 3,086*** 0,371
g_monov_ 1,163 1,078 1,312 0,905 0,851 0,941 0,250 3,086*** 0,371
*,**,*** denotes significance on the 1%, 5%,10% critical level respectively
Introduction
Economics and Econometrics
ComputationalApproach
CompetitionSetup
CompetitionResults
Conclusion
23
MICEMICE
Forecasting the EMU Inflation Rate
University of MuensterGermany
Winner Model: GENEFER Real Output Gap
-0.01
0.00
0.01
0.02
0.03
0.04
1 2 3 4 5 6 7 8 9 10 11 12 13
DLCPI GENMGAP_EC
Introduction
Economics and Econometrics
ComputationalApproach
CompetitionSetup
CompetitionResults
Conclusion
24
MICEMICE
Forecasting the EMU Inflation Rate
University of MuensterGermany
Best Econometric Model: Monetary Overhang
-0.01
0.00
0.01
0.02
0.03
0.04
1 2 3 4 5 6 7 8 9 10 11 12 13
DLCPI MOV
Introduction
Economics and Econometrics
ComputationalApproach
CompetitionSetup
CompetitionResults
Conclusion
25
MICEMICE
Forecasting the EMU Inflation Rate
University of MuensterGermany
Parametric Test Statistics
• good forecasting performance for almost all GENEFER models
ygap
_tre
ndyg
ap_h
pyg
ap_c
dm
arku
p
mon
ovm
gap
econ
omet
ric
com
put.
1st
ep
com
put.
2st
ep
0
0,5
1
1,5
2
Rel. MAE
ygap
_tre
ndyg
ap_h
pyg
ap_c
dm
arku
p
mon
ovm
gap
econ
omet
ric
com
put.
1st
ep
com
put.
2st
ep
00,20,40,60,8
11,21,4
Theil's U
Introduction
Economics and Econometrics
ComputationalApproach
CompetitionSetup
CompetitionResults
Conclusion
26
MICEMICE
Forecasting the EMU Inflation Rate
University of MuensterGermany
Non-Parametric Test Statistics
• GENEFER models outperform the econometric approaches on average
• five GENEFER models pass the Chi-squared test (Yates corrected: two), while non of the econometric ones does
• CR falls below the values of 1-step-ahead forecasts
ygap
_tre
ndyg
ap_h
pyg
ap_c
dm
arku
p
mon
ov
mga
p
econ
omet
ric
com
put.
1st
ep
com
put.
2st
ep
0
0,1
0,2
0,3
0,4
0,5
0,6
Confusion RateIntroduction
Economics and Econometrics
ComputationalApproach
CompetitionSetup
CompetitionResults
Conclusion
27
MICEMICE
Forecasting the EMU Inflation Rate
University of MuensterGermany
General Comparison
• econometric models: smaller MAPE and MAE values
• GENEFER: better with respect to RMSE (quadratic loss function!)
good average fit vs. good outlier performance
time
p
time
pa) b)
Introduction
Economics and Econometrics
ComputationalApproach
CompetitionSetup
CompetitionResults
Conclusion
28
MICEMICE
Forecasting the EMU Inflation Rate
University of MuensterGermany
Some Economic Findings
• both monetary models show better performance than real activity models (support for monetarist theories of inflation)
• real output gap model
poor parametric accuracy, but ...
... manages to predict the direction change in inflation correctly
Introduction
Economics and Econometrics
ComputationalApproach
CompetitionSetup
CompetitionResults
Conclusion
29
MICEMICE
Forecasting the EMU Inflation Rate
University of MuensterGermany
Promising Cooperation
• cooperative GENEFER models (inclusion of disequilibrium terms derived from cointegration analysis) outclass their delta rivals
outcome of the competition:not GENEFER or econometrics,
but GENEFER with econometrics!
Introduction
Economics and Econometrics
ComputationalApproach
CompetitionSetup
CompetitionResults
Conclusion
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