Forecasting the EMU Inflation Rate

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• Forecasting the EMU Inflation Rate
• Linear EconometricsVersusNon-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

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Outline

• Introduction
• Economics and Econometrics
• Computational Approach (GENEFER)
• Competition Setup
• Competition Results
• Conclusion

Introduction Economics and Econometrics Computatio
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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

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Conclusion
hereunrestricted VARsingle equation model
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Long Term Inflation Pressure Measures

• Real Activity Models
• output gap (Phillips curve)ygap y yy (i)
  trend, (ii), HP-filter, (iii) Cobb-Douglas PF
• mark-up pricingmarkup p plr plr ß1
  ß2ulclr ß3pimlr
• Monetary Models
• real money gap (price gap)mgap (m-p)
  (m-p)(m-p) ß1 ß2y ß3r
• monetary overhang (P-star)monov (m-p)
  (m-p)lr (m-p)lr ß1 ß2y ß3r

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Expectations and Short Term Disturbances

• Expectational ComponentE(?) (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)

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Econometric Modelling

• Step 1long run relationships via conintegration
  analysis(dynamic single-equation ARDL approach)
• Step 2ordinary least squares using
  error-correction terms from step 1
• ? ?D ?E(?) ?ecm ?z ?

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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
  Bundesbanks inflation objective (BIS study)

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Econometric Models In-sample-fit
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Standard Error of Regression
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Modelling Expectations in Economics (with and
without GENEFER)
Introduction Economics and Econometrics Computatio
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Conclusion
rationalexpectations
very high
limit of information processing
adaptivefuzzy rule-basedexpectations
abilityto learn
boundary to knowledge
autoregressiveexpectations
verylow
complete
none
knowledge
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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

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Linguistic Rules and Fuzzification

• IF the monetary overhang is medium AND expected
  inflation is very high THEN future inflation is
  high.

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Aggregation

• IF the monetary overhang is medium AND expected
  inflation is very high THEN future inflation is
  high.

Introduction Economics and Econometrics Computatio
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Conclusion

• ?(monetary overhang is medium) 0.6
• ?(expected inflation is very high) 0.4
• ?(antecedent) 0.4 minimum AND
• ?(antecedent) 0.32 product AND

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Inference and Defuzzification

• IF the monetary overhang is medium AND expected
  inflation is very high THEN future inflation is
  high.

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Conclusion
verylow
low
medium
high
veryhigh
?
1
0.4
0
future inflation
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Accumulation
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Fuzzy Inference Result Set and Defuzzification
Introduction Economics and Econometrics Computatio
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verylow
low
medium
high
veryhigh
?
1
0
future inflation
4.6
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Knowledge Base
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FRB Learning What?

• adapt fuzzy set widths and centers

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• reinforce (forget) used (unused) rules

• search for (new) rules

(2)
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Technology Mix for FRB Learning
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GENEFERGenetic Neural Fuzzy Explorer
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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

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Competition Setup

• 4-steps-ahead forecast
• 19 Competitors
• 7 econometric
• 11 computational
• 1 benchmark (AR(1))
• Classification
• modelling technique
• inflation indicator

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Competition Criteria (Test Statistics)

• Parametric
• mean squared error (MSE)
• root mean squared error (RMSE)
• mean absolute percentage error (MAPE)
• Theils U with an AR(1)
• relative mean absolute error (Rel. MAE)
• ?Theils U
• Non-Parametric
• confusion rate (CR)
• Chi-squared test for independence of 2?2
  confusion matrix (Yates corrected)

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Competition Results (Overview)
Introduction Economics and Econometrics Computatio
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,, denotes significance on the 1, 5,10
critical level respectively
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Winner Model GENEFER Real Output Gap
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Best Econometric Model Monetary Overhang
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Parametric Test Statistics

• good forecasting performance for almost all
  GENEFER models

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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

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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

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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

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Promising Cooperation

• cooperative GENEFER models (inclusion of
  disequilibrium terms derived from cointegration
  analysis) outclass their delta rivals
• outcome of the competitionnot GENEFER or
  econometrics,but GENEFER with econometrics!

Introduction Economics and Econometrics Computatio
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