1. 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 Muenster Institute for Computational Economics University of Muenster/Germany

2. MICE Forecasting the EMU Inflation Rate University of Muenster Germany 2 Outline Introduction Economics and Econometrics Computational Approach (GENEFER) Competition Setup Competition Results Conclusion Introduction Economics and Econometrics Computational Approach Competition Setup Competition Results Conclusion

3. MICE Forecasting the EMU Inflation Rate University of Muenster Germany 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 here: unrestricted VAR single equation model Introduction Economics and Econometrics Computational Approach Competition Setup Competition Results Conclusion

4. MICE Forecasting the EMU Inflation Rate University of Muenster Germany 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 pricing markup = p – p lr p lr = β 1 + β 2 ulc lr + β 3 pim lr Monetary Models  real money gap (price gap) mgap = (m-p) – (m-p)* (m-p)* = β 1 + β 2 y* + β 3 r*  monetary overhang (P-star) monov = (m-p) – (m-p) lr (m-p) lr = β 1 + β 2 y + β 3 r Introduction Economics and Econometrics Computational Approach Competition Setup Competition Results Conclusion

5. MICE Forecasting the EMU Inflation Rate University of Muenster Germany 5 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 Computational Approach Competition Setup Competition Results Conclusion

6. MICE Forecasting the EMU Inflation Rate University of Muenster Germany 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 Computational Approach Competition Setup Competition Results Conclusion

7. MICE Forecasting the EMU Inflation Rate University of Muenster Germany 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 Computational Approach Competition Setup Competition Results Conclusion

8. MICE Forecasting the EMU Inflation Rate University of Muenster Germany 8 Econometric Models: In-sample-fit ModelVariables R 2 (SEE) * ygap_trendD, ygap_trend(t–1), E(π), de(t–1), doil(t) 0,8864 (0,0075) ygap_hpD, ygap_hp(t–1), E(π), de(t–1), doil(t) 0,8674 (0,0081) ygap_cdD, ygap_cd(t–1), E(π), de(t–1), doil(t) 0,8674 (0,0081) monovD, monov(t–1), E(π), de(t–1), doil(t) 0,8654 (0,0083) markupD, markup(t–1), E(π), de(t–1), doil(t) 0,8993 (0,0067) mgapD, mgap(t–1), E(π), de(t–1), doil(t) 0,8433 (0,0078) eclectic D, 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 Computational Approach Competition Setup Competition Results Conclusion

9. MICE Forecasting the EMU Inflation Rate University of Muenster Germany 9 Modelling Expectations in Economics (with and without GENEFER) complete very high very low none knowledge ability to learn autoregressive expectations rational expectations limit of information processing boundary to knowledge adaptive fuzzy rule-based expectations Introduction Economics and Econometrics Computational Approach Competition Setup Competition Results Conclusion

10. MICE Forecasting the EMU Inflation Rate University of Muenster Germany 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)  adaptive fuzzy rule-based approach Introduction Economics and Econometrics Computational Approach Competition Setup Competition Results Conclusion

11. MICE Forecasting the EMU Inflation Rate University of Muenster Germany 11 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 4.5 2.0 0.2 mediumhighlow Introduction Economics and Econometrics Computational Approach Competition Setup Competition Results Conclusion

12. MICE Forecasting the EMU Inflation Rate University of Muenster Germany 12 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 Computational Approach Competition Setup Competition Results Conclusion

13. MICE Forecasting the EMU Inflation Rate University of Muenster Germany 13 Inference and Defuzzification IF the monetary overhang is medium AND expected inflation is very high THEN future inflation is high. future inflation  1 0 very low lowmediumhigh very high 0.4 Introduction Economics and Econometrics Computational Approach Competition Setup Competition Results Conclusion

14. MICE Forecasting the EMU Inflation Rate University of Muenster Germany 14 Accumulation IF... AND...THEN... Output IF... AND...THEN...    Introduction Economics and Econometrics Computational Approach Competition Setup Competition Results Conclusion

15. MICE Forecasting the EMU Inflation Rate University of Muenster Germany 15 Fuzzy Inference Result Set and Defuzzification future inflation  1 0 very low lowmediumhigh very high 4.6 % Introduction Economics and Econometrics Computational Approach Competition Setup Competition Results Conclusion

16. MICE Forecasting the EMU Inflation Rate University of Muenster Germany 16 Knowledge Base Introduction Economics and Econometrics Computational Approach Competition Setup Competition Results Conclusion

17. MICE Forecasting the EMU Inflation Rate University of Muenster Germany 17 FRB Learning: What? (1)adapt fuzzy set widths and centers w1w1 IFANDTHEN w2w2 IFANDTHEN w3w3 IFANDTHEN w4w4 IFANDTHEN w5w5 IFANDTHEN w6w6 IFANDTHEN w7w7 IFANDTHEN (1) (2) (3) (2)reinforce (forget) used (unused) rules (3)search for (new) rules Introduction Economics and Econometrics Computational Approach Competition Setup Competition Results Conclusion

18. MICE Forecasting the EMU Inflation Rate University of Muenster Germany 18 Technology Mix for FRB Learning GENEFER = Genetic Neural Fuzzy Explorer Introduction Economics and Econometrics Computational Approach Competition Setup Competition Results Conclusion

19. MICE Forecasting the EMU Inflation Rate University of Muenster Germany 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 Computational Approach Competition Setup Competition Results Conclusion

20. MICE Forecasting the EMU Inflation Rate University of Muenster Germany 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 Computational Approach Competition Setup Competition Results Conclusion

21. MICE Forecasting the EMU Inflation Rate University of Muenster Germany 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 Computational Approach Competition Setup Competition Results Conclusion

22. MICE Forecasting the EMU Inflation Rate University of Muenster Germany 22 Competition Results (Overview) ModelMSERMSEMAPE Rel. MAE Theil’s U Theil’s U CR  2 (1)  2 Yates AR(1)1,6041,2671,312110,9740,500,333 ygap_trend1,0741,0370,9841,0050,8180,9380,4170,3430,000 ygap_hp2,1351,4611,4461,4931,1541,3110,4170,3430,000 ygap_cd2,0201,4211,3831,4451,1221,2770,4170,3430,000 monov0,7710,8780,6990,8480,6930,8160,4170,3430,375 markup1,0341,0170,7420,8780,8030,9700,4170,3430,000 mgap0,5690,7540,5210,6920,5950,7100,5000,3430,333 eclectic1,0991,0480,6790,9230,8280,9930,4170,3430,000 g_ygaptrend1,3721,1711,4201,0990,9251,0890,4170,3430,000 g_ygaphp1,8521,3611,0751,8491,1361,1740,3341,3340,333 g_ygapcd2,2331,4931,1802,0001,2261,3490,1675,333**3,000** * g_monov1,2691,1270,9761,0150,8900,8840,2503,086***1,371 g_markup1,1661,0801,3380,9880,8530,9830,2503,086***1,371 g_mgap0,5310,7290,7940,6750,5750,6290,1675,333**3,000** * g_eclectic1,1141,0550,8220,9680,8330,9990,6671,3330,333 g_eclectic_ 0,8540,9241,0010,8410,7300,8060,3331,5000,375 g_markup_ 0,9230,9610,9450,9110,7590,9050,5830,3430,000 g_mgap_ 0,9210,9601,0830,8540,7580,8620,2503,086***0,371 g_monov_ 1,1631,0781,3120,9050,8510,9410,2503,086***0,371 *,**,*** denotes significance on the 1%, 5%,10% critical level respectively Introduction Economics and Econometrics Computational Approach Competition Setup Competition Results Conclusion

23. MICE Forecasting the EMU Inflation Rate University of Muenster Germany 23 Winner Model: GENEFER Real Output Gap Introduction Economics and Econometrics Computational Approach Competition Setup Competition Results Conclusion

24. MICE Forecasting the EMU Inflation Rate University of Muenster Germany 24 Best Econometric Model: Monetary Overhang Introduction Economics and Econometrics Computational Approach Competition Setup Competition Results Conclusion

25. MICE Forecasting the EMU Inflation Rate University of Muenster Germany 25 Parametric Test Statistics good forecasting performance for almost all GENEFER models Introduction Economics and Econometrics Computational Approach Competition Setup Competition Results Conclusion

26. MICE Forecasting the EMU Inflation Rate University of Muenster Germany 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 Computational Approach Competition Setup Competition Results Conclusion

27. MICE Forecasting the EMU Inflation Rate University of Muenster Germany 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 Computational Approach Competition Setup Competition Results Conclusion

28. MICE Forecasting the EMU Inflation Rate University of Muenster Germany 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 Computational Approach Competition Setup Competition Results Conclusion

29. MICE Forecasting the EMU Inflation Rate University of Muenster Germany 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 Computational Approach Competition Setup Competition Results Conclusion