Applied Econometric Time Series

498 Pages·2014·6.94 MB·English

by  Walter Enders

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FOURTHEDITION
APPLIED
ECONOMETRIC
TIME SERIES
WALTER ENDERS
UniversityofAlabama
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LibraryofCongressCataloging-in-PublicationData
Enders,Walter,1948-
Appliedeconometrictimeseries/Walter,UniversityofAlabama.–Fourthedition.
pagescm
Includesindex.
ISBN978-1-118-80856-6(pbk.)
1. Econometrics.2. Time-seriesanalysis.I.Title.
HB139.E552015
330.01’519233–dc23
2014013428
PrintedintheUnitedStatesofAmerica
10 9 8 7 6 5 4 3 2 1
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ToLola
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CONTENTS
PREFACE vii
ABOUTTHEAUTHOR x
CHAPTER1 DIFFERENCEEQUATIONS 1
Introduction 1
1 Time-SeriesModels 1
2 DifferenceEquationsandTheirSolutions 7
3 SolutionbyIteration 10
4 AnAlternativeSolutionMethodology 14
5 TheCobwebModel 18
6 SolvingHomogeneousDifferenceEquations 22
7 ParticularSolutionsforDeterministicProcesses 31
8 TheMethodofUndeterminedCoefficients 34
9 LagOperators 40
10 Summary 43
QuestionsandExercises 44
CHAPTER2 STATIONARYTIME-SERIESMODELS 47
1 StochasticDifferenceEquationModels 47
2 ARMAModels 50
3 Stationarity 51
4 StationarityRestrictionsforanARMA(p,q)Model 55
5 TheAutocorrelationFunction 60
6 ThePartialAutocorrelationFunction 64
7 SampleAutocorrelationsofStationarySeries 67
8 Box–JenkinsModelSelection 76
9 PropertiesofForecasts 79
10 AModeloftheInterestRateSpread 88
11 Seasonality 96
12 ParameterInstabilityandStructuralChange 102
13 CombiningForecasts 109
14 SummaryandConclusions 112
QuestionsandExercises 113
iv
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CONTENTS v
CHAPTER3 MODELINGVOLATILITY 118
1 EconomicTimeSeries:TheStylizedFacts 118
2 ARCHandGARCHProcesses 123
3 ARCHandGARCHEstimatesofInflation 130
4 ThreeExamplesofGARCHModels 134
5 AGARCHModelofRisk 141
6 TheARCH-MModel 143
7 AdditionalPropertiesofGARCHProcesses 146
8 MaximumLikelihoodEstimationofGARCHModels 152
9 OtherModelsofConditionalVariance 154
10 EstimatingtheNYSEU.S.100Index 158
11 MultivariateGARCH 165
12 VolatilityImpulseResponses 172
13 SummaryandConclusions 174
QuestionsandExercises 176
CHAPTER4 MODELSWITHTREND 181
1 DeterministicandStochasticTrends 181
2 RemovingtheTrend 189
3 UnitRootsandRegressionResiduals 195
4 TheMonteCarloMethod 200
5 Dickey–FullerTests 206
6 ExamplesoftheDickey–FullerTest 210
7 ExtensionsoftheDickey–FullerTest 215
8 StructuralChange 227
9 PowerandtheDeterministicRegressors 235
10 TestswithMorePower 238
11 PanelUnitRootTests 243
12 TrendsandUnivariateDecompositions 247
13 SummaryandConclusions 254
QuestionsandExercises 255
CHAPTER5 MULTIEQUATIONTIME-SERIESMODELS 259
1 InterventionAnalysis 261
2 ADLsandTransferFunctions 267
3 AnADLofTerrorisminItaly 277
4 LimitstoStructuralMultivariateEstimation 281
5 IntroductiontoVARAnalysis 285
6 EstimationandIdentification 290
7 TheImpulseResponseFunction 294
8 TestingHypotheses 303
9 ExampleofaSimpleVAR:DomesticandTransnationalTerrorism 309
10 StructuralVARs 313
11 ExamplesofStructuralDecompositions 317
12 OveridentifiedSystems 321
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vi CONTENTS
13 TheBlanchard–QuahDecomposition 325
14 DecomposingRealandNominalExchangeRates:AnExample 331
15 SummaryandConclusions 335
QuestionsandExercises 337
CHAPTER6 COINTEGRATIONANDERROR-CORRECTIONMODELS 343
1 LinearCombinationsofIntegratedVariables 344
2 CointegrationandCommonTrends 351
3 CointegrationandErrorCorrection 353
4 TestingforCointegration:TheEngle–GrangerMethodology 360
5 IllustratingtheEngle–GrangerMethodology 364
6 CointegrationandPurchasingPowerParity 370
7 CharacteristicRoots,Rank,andCointegration 373
8 HypothesisTesting 380
9 IllustratingtheJohansenMethodology 389
10 Error-CorrectionandADLTests 393
11 ComparingtheThreeMethods 397
12 SummaryandConclusions 400
QuestionsandExercises 401
CHAPTER7 NONLINEARMODELSANDBREAKS 407
1 LinearVersusNonlinearAdjustment 408
2 SimpleExtensionsoftheARMAModel 410
3 TestingforNonlinearity 413
4 ThresholdAutoregressiveModels 420
5 ExtensionsoftheTARModel 427
6 ThreeThresholdModels 433
7 SmoothTransitionModels 439
8 OtherRegimeSwitchingModels 445
9 EstimatesofSTARModels 449
10 GeneralizedImpulseResponsesandForecasting 453
11 UnitRootsandNonlinearity 461
12 MoreonEndogenousStructuralBreaks 466
13 SummaryandConclusions 474
QuestionsandExercises 475
INDEX 479
REFERENCES(ONLINE)
ENDNOTES(ONLINE)
STATISTICALTABLES(ONLINE)
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PREFACE
When I began writing the first edition, my intent was to write a text in time-series
macroeconometrics.Fortunately,anumberofmycolleaguesconvincedmetobroaden
the focus. Applied microeconomists have embraced time-series methods, and the
politicalsciencejournalshavebecomemorequantitative.Asinthepreviouseditions,
examples are drawn from macroeconomics, agricultural economics, international
finance, and my work with Todd Sandler on the study of domestic and transnational
terrorism.Youshouldfindthattheexamplesinthetextprovideareasonablebalance
betweenmacroeconomicandmicroeconomicapplications.
1. BACKGROUND
Thetextisintendedforthosewithsomebackgroundinmultipleregressionanalysis.
Ipresumethereaderunderstandstheassumptionsunderlyingtheuseofordinaryleast
squares.Allofmystudentsarefamiliarwiththeconceptscorrelationandcovariation;
theyalsoknowhowtouset-testsandF-testsinaregressionframework.Iusetermssuch
asmeansquareerror,significancelevel,andunbiasedestimatewithoutexplainingtheir
meaning. Twochaptersofthetextexaminemultipletime-seriestechniques.Towork
through these chapters, it is necessary to know how to solve a system of equations
using matrix algebra. Chapter 1, entitled “Difference Equations,” is the cornerstone
of the text. In my experience, this material and a knowledge of regression analysis
aresufficienttobringstudentstothepointwheretheyareabletoreadtheprofessional
journalsandtoembarkonaseriousappliedstudy.Nevertheless,oneunfortunatereader
wrote,“Idideverythingyousaidinyoubook,andmyarticlestillgotrejected.”
Some of the techniques illustrated in the text need to be explicitly programmed.
StructuralVARsneedtobeestimatedusingapackagethathasthecapacitytomanip-
ulate matrices. Monte Carlo methods are very computer intensive. Nonlinear models
needtobeestimatedusingapackagethatcanperformnonlinearleastsquaresandmax-
imumlikelihoodestimation.Completelymenu-drivensoftwarepackagesarenotable
toestimateeveryformoftime-seriesmodel.AsItellmystudents,bythetimeapro-
cedureappearsonthemenuofaneconometricsoftwarepackage,itisnotnew.Toget
themostfromthetext,youshouldhaveaccesstoaprogramsuchasEViews,RATS,
MATLAB,R,STATA,SAS,orGAUSS.
I take the term applied that appears in the title earnestly. Toward this end,
I believe in teaching by induction. The method is to take a simple example and
buildtowardmoregeneralandmorecomplicatedmodels.Detailedexamplesofeach
procedure are provided. Each concludes with a step-by-step summary of the stages
typicallyemployedinusingthatprocedure.Theapproachisoneoflearningbydoing.
vii
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viii PREFACE
A large number of solved problems are included in the body of each chapter.
The “Questions and Exercises” section at the end of each chapter is especially
important.Youareencouragedtoworkthroughasmanyoftheexamplesandexercises
aspossible.
2. WHAT IS NEW IN THE FOURTH EDITION?
Ihave triedtobecarefulabout thetrade-offbetween beingcompleteandbeingcon-
cise. In deciding on which new topics to include in the text, I relied heavily on the
e-mailmessagesIreceivedfrominstructorsandfromstudents.Tokeepthemanuscript
from becoming encyclopedic, I have included a number of new topics in the Sup-
plementary Manual. The new material in Chapter 2 discusses the important issue of
combining multiple univariate forecasts so as to reduce overall forecast error vari-
ance.Chapter3expandsthediscussionofmultivariateGARCHmodelsbyillustrating
volatilityimpulseresponsefunctions.Indoingso,volatilityspilloversneedtobeana-
lyzed in a way that is analogous to the impulse responses from a VAR. I received a
surprisinglylargenumberofquestionsregardingautoregressivedistributedlag(ADL)
models.Assuch,thefirstfewpartsofChapter5havebeenrewrittensoastoshowthe
appropriatewaystoproperlyidentifyandestimateADLs.Thisnewmaterialcomple-
mentsthematerialinChapter 6involvingADLsinacointegrated system.Chapter 7
nowdiscussestheso-calledDaviesprobleminvolvingunidentifiednuisanceparame-
tersunderthenullhypothesis.Thechaptercontinuestodiscusstheissuesinvolvedwith
testingformultipleendogenousbreaks(i.e.,potentialbreaksoccurringatanunknown
date)usingtheBai–Perronprocedure.Moreover,sincebreakscanmanifestthemselves
slowly,theprocessofestimatingamodelwithalogisticbreakisillustrated.
SomecontenthasbeenmovedtothewebsitefortheFourthEdition.Thiscontent
is called out in the Table of Contents as being “online.” To locate this content, go to
Wiley.com/College/Endersortotime-series.net.
3. ADDITIONAL MATERIALS
Sinceitwasnecessarytoexcludesometopicsfromthetext,IpreparedaSupplementary
Manualtothetext.ThismanualcontainsmaterialthatIdeemedimportant(orinterest-
ing),butnotsufficientlyimportantforallreaders,toincludeinthetext.Oftenthetext
refersyoutothisSupplementaryManualtoobtainadditionalinformationonatopic.
Toassistyouinyourprogramming,IhavewrittenaRATSProgrammingManual
toaccompanythistext.Ofcourse,itisimpossibleformetohaveversionsoftheguide
foreverypossibleplatform.Mostprogrammersshouldbeabletotranscribeaprogram
writteninRATSintothelanguageusedbytheirpersonalsoftwarepackage.
An Instructors’ Manual is available to those adopting the text for their class.
Themanualcontainstheanswerstoallofthemathematicalquestions.Italsocontains
programs that can be used to reproduce most of the results reported in the text and
allofthemodelsindicatedinthe“QuestionsandExercises”sections.Versionsofthe
manualareavailableforEVIEWS,RATS,SAS,andSTATAusers.