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Forecasting the EMU Inflation Rate Linear Econometrics Versus Non-Linear Computational Models

Forecasting the EMU Inflation Rate Linear Econometrics Versus Non-Linear Computational Models The 2003 International Conference on Artificial Intelligence, Las Vegas, USA Applications of AI in Finance & Economics Stefan Kooths, Timo Mitze, Eric Ringhut

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Forecasting the EMU Inflation Rate Linear Econometrics Versus Non-Linear Computational Models

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  1. 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

  2. Outline • Introduction • Economics and Econometrics • Computational Approach (GENEFER) • Competition Setup • Competition Results • Conclusion Introduction Economics and Econometrics ComputationalApproach CompetitionSetup CompetitionResults Conclusion

  3. 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 Introduction Economics and Econometrics ComputationalApproach CompetitionSetup CompetitionResults Conclusion here:unrestricted VARsingle equation model

  4. 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 – plrplr = 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. 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) Introduction Economics and Econometrics ComputationalApproach CompetitionSetup CompetitionResults Conclusion

  6. 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. 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. Econometric Models: In-sample-fit Introduction Economics and Econometrics ComputationalApproach CompetitionSetup CompetitionResults Conclusion *Standard Error of Regression

  9. Modelling Expectations in Economics (with and without GENEFER) Introduction Economics and Econometrics ComputationalApproach CompetitionSetup CompetitionResults Conclusion rationalexpectations very high limit of information processing adaptivefuzzy rule-basedexpectations abilityto learn boundary to knowledge autoregressiveexpectations verylow none complete knowledge

  10. 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) • adaptivefuzzyrule-based approach Introduction Economics and Econometrics ComputationalApproach CompetitionSetup CompetitionResults Conclusion

  11. low medium high 1 0.6 0.2 0 monov 3.8 2.0 4.5 Linguistic Rules and Fuzzification IF the monetary overhang is mediumAND expected inflation is very highTHEN future inflation is high. Introduction Economics and Econometrics ComputationalApproach CompetitionSetup CompetitionResults Conclusion

  12. Aggregation IF the monetary overhang is mediumAND expected inflation is very highTHEN future inflation is high. Introduction Economics and Econometrics ComputationalApproach CompetitionSetup CompetitionResults Conclusion • (monetary overhang is medium) = 0.6 • (expected inflation is very high) = 0.4 • (antecedent) = 0.4 [minimum AND] • (antecedent) = 0.32 [product AND]

  13. Inference and Defuzzification IF the monetary overhang is mediumAND expected inflation is very highTHEN future inflation is high. Introduction Economics and Econometrics ComputationalApproach CompetitionSetup CompetitionResults Conclusion verylow low medium high veryhigh  1 0.4 0 future inflation

  14. 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... Accumulation Introduction Economics and Econometrics ComputationalApproach CompetitionSetup CompetitionResults Conclusion

  15. Fuzzy Inference Result Set and Defuzzification Introduction Economics and Econometrics ComputationalApproach CompetitionSetup CompetitionResults Conclusion verylow low medium high veryhigh  1 0 future inflation 4.6 %

  16. Knowledge Base Introduction Economics and Econometrics ComputationalApproach CompetitionSetup CompetitionResults Conclusion

  17. (1) (3) FRB Learning: What? • adapt fuzzy set widths and centers Introduction Economics and Econometrics ComputationalApproach CompetitionSetup CompetitionResults Conclusion reinforce (forget) used (unused) rules • search for (new) rules (2)

  18. Technology Mix for FRB Learning Introduction Economics and Econometrics ComputationalApproach CompetitionSetup CompetitionResults Conclusion GENEFER=Genetic Neural Fuzzy Explorer

  19. 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 Introduction Economics and Econometrics ComputationalApproach CompetitionSetup CompetitionResults Conclusion

  20. Competition Setup • 4-steps-ahead forecast • 19 Competitors • 7 econometric • 11 computational • 1 benchmark (AR(1)) • Classification • modelling technique • inflation indicator Introduction Economics and Econometrics ComputationalApproach CompetitionSetup CompetitionResults Conclusion

  21. 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 22 confusion matrix (Yates corrected) Introduction Economics and Econometrics ComputationalApproach CompetitionSetup CompetitionResults Conclusion

  22. Competition Results (Overview) Introduction Economics and Econometrics ComputationalApproach CompetitionSetup CompetitionResults Conclusion *,**,*** denotes significance on the 1%, 5%,10% critical level respectively

  23. Winner Model: GENEFER Real Output Gap Introduction Economics and Econometrics ComputationalApproach CompetitionSetup CompetitionResults Conclusion

  24. Best Econometric Model: Monetary Overhang Introduction Economics and Econometrics ComputationalApproach CompetitionSetup CompetitionResults Conclusion

  25. Parametric Test Statistics • good forecasting performance for almost all GENEFER models Introduction Economics and Econometrics ComputationalApproach CompetitionSetup CompetitionResults Conclusion

  26. 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 Introduction Economics and Econometrics ComputationalApproach CompetitionSetup CompetitionResults Conclusion

  27. 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 Introduction Economics and Econometrics ComputationalApproach CompetitionSetup CompetitionResults Conclusion

  28. 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. 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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