forecasting the emu inflation rate linear econometrics versus non-linear computational models the...

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

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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

here:unrestricted VAR

single equation model

Introduction



CompetitionSetup

CompetitionResults

Conclusion

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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



CompetitionSetup

CompetitionResults

Conclusion

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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



CompetitionSetup

CompetitionResults

Conclusion

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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



CompetitionSetup

CompetitionResults

Conclusion

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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 Bundesbank‘s inflation objective (BIS study)

Introduction



CompetitionSetup

CompetitionResults

Conclusion

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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



CompetitionSetup

CompetitionResults

Conclusion

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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



CompetitionSetup

CompetitionResults

Conclusion

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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

Introduction



CompetitionSetup

CompetitionResults

Conclusion

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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.

monov

1

0

3.8

0.6

4.52.0

0.2

medium highlow

Introduction



CompetitionSetup

CompetitionResults

Conclusion

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Aggregation


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



CompetitionSetup

CompetitionResults

Conclusion

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Inference and Defuzzification


inflation is high.

future inflation

1

0

verylow low medium high

veryhigh

0.4

Introduction



CompetitionSetup

CompetitionResults

Conclusion

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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



CompetitionSetup

CompetitionResults

Conclusion

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Fuzzy Inference Result Set and Defuzzification

future inflation

1

0

verylow low medium high

veryhigh

4.6 %

Introduction



CompetitionSetup

CompetitionResults

Conclusion

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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


Introduction



CompetitionSetup

CompetitionResults

Conclusion

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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



CompetitionSetup

CompetitionResults

Conclusion

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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)


1 low medium medium




5 low low low



8 medium low low



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



CompetitionSetup

CompetitionResults

Conclusion

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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

FilteringPerceivedreality


1 low medium medium




5 low low low



8 medium low low



crisp fuzzy-rule-base

output

Direction of information processing

linguistic levelnumeric level numeric level

Introduction



CompetitionSetup

CompetitionResults

Conclusion

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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

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



CompetitionSetup

CompetitionResults

Conclusion

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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



CompetitionSetup

CompetitionResults

Conclusion

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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



CompetitionSetup

CompetitionResults

Conclusion

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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



CompetitionSetup

CompetitionResults

Conclusion

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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



CompetitionSetup

CompetitionResults

Conclusion

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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



CompetitionSetup

CompetitionResults

Conclusion

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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

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



CompetitionSetup

CompetitionResults

Conclusion

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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

time

p

time

pa) b)

Introduction



CompetitionSetup

CompetitionResults

Conclusion

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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

Introduction



CompetitionSetup

CompetitionResults

Conclusion

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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



CompetitionSetup

CompetitionResults

Conclusion

forecasting the emu inflation rate linear econometrics versus non-linear computational models the...

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forecasting emu inflation

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