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【正文】 nded cycles with varying lengthsVarying length of deautocorrelations from varying length of time windows TAFD TAHP TALLDWhite Noise (35%) vs. Persistent Cycles (65%)Correlation dimension =Color chaos (strange attractor)Crosscorrelation = Phase portraits of SP 500 HPc cyclesWhite image vs. color chaosUncertainty Principle in Signal ProcessingGabor (Gaussian) Wavelet with Minimum UncertaintyGabor Space (1946) in discrete timefrequency space? Minimum uncertainty in timefrequency space? Unorthogonal base functionSeparating signals and noise in Gabor (timefrequency) spacePrinciple of Large Numbers for Positive Variables ? SN=X1+X2+ . . . . . . +XN Observed relative deviation of US real GDP is 20 times larger than Lucas model( Chen 2023)!Observed MV 》 Effective CN (Data Source: Fed. Reserve St. Louis)Real Personal consumption: % (800,000)? Real GDP: % (500,000)? Real Private Investment: % (10,000)? Dow Jones Industrial (192809): % (9,000)? SP 500 Index (19472023): % (5,000)? NASDAQ (19712023): % (3,000)? JapanUS Exchange Rate (197109) % (300)
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