Evaluating Econometric Forecasts of Economic and Financial Variables

187 Pages·2005·1.024 MB·English

by  Michael P. Clements (auth.)

Evaluating Econometric
Forecasts of Economic and
Financial Variables
Michael P. Clements
Evaluating Econometric Forecasts of Economic
and Financial Variables
PalgraveTextsinEconometrics
SeriesEditor:KerryPatterson
Titlesinclude:
SimonP.Burke
MODELLINGNON-STATIONARYECONOMICTIMESERIES
MichaelP.Clements
EVALUATINGECONOMETRICFORECASTSOFECONOMICAND
FINANCIALVARIABLES
TerenceC.Mills
MODELLINGTRENDSANDCYCLESINECONOMICTIMESERIES
KerryPatterson
UNITROOTSINECONOMICTIMESERIES
JanPodivinsky
MODELLINGVOLATILITY
PalgraveTextsinEconometrics
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Evaluating Econometric
Forecasts of Economic and
Financial Variables
Michael P. Clements
UniversityofWarwick
©MichaelP.Clements2005
Softcover reprint of the hardcover 1st edition 2005 978-1-4039-4156-5
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Clements,MichaelP.
Evaluatingeconometricforecastsofeconomicandfinancial
variables/MichaelP.Clements.
p.cm.–(Palgravetextsineconometrics)
Includesbibliographicalreferencesandindex.
1.Economicforecasting–Econometricmodels–Evaluation.
I.Title.II.Series.
HB3730.C5562005
330(cid:2).01(cid:2)5195—dc22 2004054893
10 9 8 7 6 5 4 3 2 1
14 13 12 11 10 09 08 07 06 05
To Carolyn, Anna and William
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Contents
ListofTables x
ListofFigures xi
Author’sPrefaceandAcknowledgements xii
1 Introduction 1
2 PointForecasts 4
2.1 Realization-forecastregressions 4
2.1.1 Testingtherationalityofmulti-stepforecasts 7
2.2 Forecastprecision 9
2.3 Rivalforecasts,forecastcombinationand
encompassing 12
2.3.1 Testsofcomparativeforecastaccuracy 12
2.3.2 Forecastcombination(orpooling)and
encompassing 15
2.4 Testingmodel-basedforecastsforpredictiveaccuracy 21
2.4.1 Testsofpredictiveaccuracy 21
2.4.2 Testsofequalaccuracyandencompassing
whenparametersareestimated 25
2.5 Non-linearmodelsandforecasting 30
2.5.1 TheconditionalexpectationistheMMSEpredictor 30
2.5.2 Multi-stepforecastsandnon-linearmodels 32
2.5.3 SETARmodelsandmulti-periodforecasts 34
2.5.4 Markov-switchingmodels 37
2.5.5 Evaluatingnon-linearmodelforecasts 39
2.6 Summary 45
3 VolatilityForecasts 46
3.1 Introduction 46
3.2 Changingconditional-variancesandoptimalpoint
forecasts 48
3.3 Time-varyingconditionalvariancesandasymmetric
loss 51
3.4 Modelsofconditionalvariance 54
3.4.1 ARCHmodels 54
3.4.2 Estimation 58
vii
viii Contents
3.4.3 GARCHmodels 59
3.4.4 GARCHmodelforecasts 62
3.4.5 IGARCH 63
3.4.6 Non-linearGARCH 64
3.4.7 GARCHandforecastsoftheconditionalmean 67
3.5 Evaluationofvolatilityforecasts 68
3.6 Recentdevelopmentsintheevaluationofvolatility
forecasts 73
3.6.1 Realizedvolatility 73
3.6.2 Intradayrange 74
3.6.3 Utility-basedmeasuresandtradingrules 75
3.7 Summary 75
4 IntervalForecasts 77
4.1 Introduction 77
4.2 Calculatingintervalforecasts 78
4.2.1 Bootstraptheforecasts 80
4.2.2 Allowingestimationuncertainty 81
4.2.3 Conditionalintervalsandestimationuncertainty 82
4.2.4 Bias-correctingtheparameterestimates 82
4.2.5 MonteCarloevaluation:step-by-stepguide 83
4.2.6 BootstrappingARCHprocesses 85
4.3 Desirablepropertiesofintervalforecasts 87
4.4 Testsforconditionalefficiency 88
4.4.1 Unbiasedness 88
4.4.2 Independence 89
4.5 Regression-basedtestsofconditionalefficiency 91
4.6 IntervalforecastconstructionandARCH 92
4.7 Empiricalillustration 94
4.7.1 Intervalforecastsandintradailydata 94
4.7.2 Propertiesoffuturesreturnsdata 95
4.8 Summary 102
5 DensityForecasts 103
5.1 Introduction 103
5.2 Probabilitydistributionforecastevaluation 104
5.3 Jointprobabilitydistributions 106
5.4 Calibration 107
5.5 Densityandintervalforecasts 108
5.6 Empiricalillustration(I):theSPFprobability
distributions 110
Contents ix
5.7 Empiricalillustration(II):theMPCinflationforecasts 112
5.7.1 Pointforecastperformance 113
5.7.2 Evaluationofforecastdensities 116
5.8 Model-baseddensityevaluation 117
5.8.1 Modelmis-specification 120
5.9 Summary 121
5.10 Appendix:multivariateforecastdensityprobability
integraltransformtests 121
6 Decision-basedEvaluation 124
6.1 Introduction 124
6.2 Decision-basedevaluation–somebasicresults 126
6.3 Quadraticlossfunctions 127
6.4 Two-state,two-actiondecisionproblems 129
6.5 Decisionproblemforinflation-targetingandinterest
ratesetting 131
6.6 Statisticalmeasuresrelatedtoeconomicvalue 133
6.7 TheBankofEnglandMPCinflationforecasts 135
6.8 Propertiesofoptimalforecastsforgeneralloss
functions 137
6.8.1 Generallossfunctionsandthegeneralized
forecasterror 140
6.9 Summary 141
7 Postscript 143
8 ComputerCode 146
8.1 SampleGausscodefortheestimationandforecastingof
SETARmodels 146
8.1.1 Extensions 147
8.2 EstimationandforecastingGARCH(1,1)processes 150
8.3 MonteCarloevaluationofintervallengthsand
coverages 151
8.3.1 Extensions 153
8.4 Forecastdensityevaluation 154
Notes 156
References 160
Index 170