HPtrendcycletp.docx
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HPtrendcycletp.docx
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HPtrendcycletp
I.Trend-CycleDecompositionand
TheCopernicusProbleminMacroEconometrics
(1.1)ThreeReferencesinTrend-CycleDecomposition
(1.2)TheHPTrend-CycleDecompositionand
theNBERBusinessCycleChronology
II.ThePatternofLargeNumbersandtheChoiceof
ThePreferredObservationReference
(2.1)TheRelativeDeviationandthePatternofLargeNumbers
(2.2)WeakEvidenceofMicrofoundationsand
StrongEvidenceofIntermediateStructure
III.EconomicCoherenceunderPersistentFluctuations
(3.1)RandomWalk,Noise-DrivenDiffusion,andTemporaryGrowth
(3.2)TheBirth-DeathProcessandEconomicCoherence
IV.WhiteNoise,ColorChaos,andPersistentCycles
(4.1)AnExponentialDampingofNoise-DrivenCycles
(4.2)PersistentCyclesandColorChaosundertheHPReference
V.Histo-GraphandEconomicDiagnosis
(5.1)TrendChangesandHistoricalEvents
(5.2)ExternalShock,InternalInstability,andFrequencyShift
VI.Conclusion:
PersistentCycles,EconomicCoherence,
AndthePreferredObservationReference
USGDPC1LnQuarterlySerieswithLog-Linear(LL)andHPTrends
GDPC1LnDetrendedCycles:
HPc,LLc,FDs
CCmax1(-4)=0.6936,Ccmin+(22)=-0.4422,CCmax2(48)=0.1503,
Ccmin-(-35)=-0.2502.InvestmenttrendchangesleadrealGDPfor1year.
CCmax1
(1)=0.8082,Ccmin+(30)=-0.2029,CCmax2(52)=0.1149,
Ccmin-(-26)=-0.3516.ConsumptiontrendchangeslagsrealGDPfor1quarter.
TheUSRealGDPHPCyclesandNBERBusinessCycleChronology
NBERBusinessCyclePeak&TroughDate
Peak11/487/538/574/6012/6911/731/807/817/90
Trough10/495/544/582/6111/703/757/8011/823/91
ComparingFDsandFDHgseriesofGDPC1LnData
Mean(FDs)~mean(FDHg)
STD(FDs)/STD(FDHg)=4.6
Peaks:
11/487/538/574/6012/6911/731/807/817/90
Troughs:
10/495/544/582/6111/703/757/8011/823/91
TheRelativeDeviationsofGDPC1LnSeries.
TableI.TheRelativeDeviationofGDPC1LnunderDifferentReferences
Data
HP
LL
ST
FD
ρ(%)
0.21
0.35
1.2
120
EC(%)
28
28
22
31
N*
200,000
80,000
7,000
0.7
RDsareaveragesin1947-2000withamovingtime-windowof10years.
TableII.TheRelativeDeviationρofMacroIndexes
ρ(%)[N*]
GDPC1Ln
PCECC965Ln
GDPIC1Ln
UNEMP
ST
1.2[7,000]
1.4[6,000]
2.4[2,000]
20.3[20]
HP
0.2[200,000]
0.17[300,000]
1.2[7,000]
N/A
EC(%)
28(HP)
25(HP)
31(HP)
24(ST)
GDPC1-thequarterlyrealGDP
GPDIC1–thequarterlyrealgrossprivatedomesticinvestment
PCECC96-thequarterlyrealpersonalconsumptionexpenditures
UNEMP-themonthlyunemploymentrate
TableIII.NumbersofHouseholdsandFirmsofUSin1980
Micro-Agents
Households
Corporations*
PublicCompanies
N
80.7(million)
2.9(million)
20,000
ρ*(%)
0.01
0.05
0.7
*Thenumberofcorporationswithmorethan$100,000inassets.
PossibleCausesofAggregatedFluctuations:
MicroFoundationsontheHousehold&FirmLevel
WeakEvidenceof
TheTwo-LevelModel(Micro-Macro)
IntermediateStructureontheFinancialMarkets&
IndustrialOrganizations
StrongEvidenceof
TheThree-LevelModel(Micro-Intermediate-Macro)
TableIV.TheFrischModelofGDPC1lnCycles
(1947Q1-2000Q3)
Detrending
β
T(yr)
T1(yr)
Tβ(yr)
σ
g
FD
0.62
1.84
1.85
3.2
0.0102
0.53
HP
0.2
4.4
4.4
10.0
0.0174
2.2
LLD
0.025
52.6
52.9
80
0.0422
74.8
TableV.TheRelativeDeviationsof
StochasticModelsofFluctuatingGrowth
ModelTypeRelativeDeviation
RandomWalkModel
=
Noise-DrivenDiffusionModel
LinearBirth&DeathProcess
ForGDPC1Lnseries,σ=0.0485,
Fort=0,rd(FP)=0;
Fort=20yrs=80qtrs,rd(FP)=0.455=45.5%;
Fort=50yrs=200qtr,rd(FP)=0.7751=77.5%;
Fort>74yrs,RDfp>100%
ThePhasePortraitsofFSPCOM(S&P500)HPCycles
WhiteNoiseorColorChaos?
T=60months.Itsfractaldimensionis2.5.
EconomicDiagnosisofTimeEvolution
OfTheBasicPeriodPb
FromtheS&P500HPCycles
Histo-Period-Graph(HPG)ofFrequencyShifts
NaturalExperimentI.Frequencyshiftoccurred
AftertheOilPriceShockinOct.1973
SignofExternalShocks
NaturalExperimentII.Frequencyshiftoccurred
BeforeandaftertheStockMarketCrashinOct.1987
SignofanInternalInstability
HPTrendGrowthRate,ExternalShocks,andGovernmentPolicies
Histo-Trend-Graph(HTG)ofTrendChanges
AverageAnnualTrendGrowthRate=3.5%
(FirstDifferenceofHPSmoothGrowthTrends)
ObservedEvolutionandPossibleCauses?
Peaks:
1953Q3(KoreanWarended)
1964Q2(VietnamWarbeganin8/64)
Twosmallpeaksin1971Q4and1976Q4
Mightbecausedbytheoilshocktroughin1973
1985Q1(NegativeOilPriceShock&ReaganRevolution)
2000Q2(Newtechnology&ClintonInnovation?
)
Troughs:
1957Q1(ModerationoftheColdWar)
1970Q1(Down-scaleinVietnamWar&NixonShock)
1974Q1(OilPriceShockat10/73)
1980Q4(OilPriceShockin79?
)
1990Q4(ColdWarEnding)
Conclusions
I.MeasurementofBusinessCycles:
TheHPTrend-CycleDecompositionIsthePreferredObservationReference
II.NewObservationsofEconomicCoherenceinMacroeconomics:
StableandLargeRelativeDeviations–EconomicCoherence
StableandNarrowFrequencyBand–PersistentCycles
III.ExistingTheoryofGrowthFluctuationsandPersistentCycles:
ProbabilityDistributionIsBetterThan
TrajectoryRepresentation
InternalFluctuationsinGrowth
AndthePatternofLargeNumbers
RandomWalkandNoise-DrivenDiffusion
HaveNoEconomicCoherence
DeterministicColorChaosinHPCycles
AndStructuralStabilityinParameterSpace
Noise-DrivenCyclesAreDampedExponentially
IV.NewDiscoveriesandNewTheories:
WeakMicroFoundationsonHouseholdandFirmLevel
StrongEvidenceofIntermediateStructures
NoPuzzleofConsumptionSmoothness
NoPersistentShocksinEconomicHistory
UncertaintyattheShort-TermandLong-TermMovements
RegularityattheMedium-TermBusinessCycles
HPcycles–Histo-Period-Graph
FDHgCycles–Histo-Trend-Graph
V.NewPerspectiveofBusinessCycleTheory:
EconomicOrganismwithBiologicalClock
NoPossibilityofMechanic‘Fine-Tune’inPolicyControl
EconomicDiagnosisIsNeededforSelf-OrganizedSystems
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