基函数与经济波动的本质: 外来噪声驱动ⅴs.内生(非线性)振子 ·描写经济动力学的基函数 白噪声,谐振波,与 wavelets Wigner transform, Gabor wavelet, and logistic wavelet 经济波动( business cycles)的本质:内生震荡还是 外来噪声驱动? Frisch model of noise driven harmonic cycles (1933), Harmonically bounded Brownian motion ( Unlenbeck& Orstein1930, Uhlenbeck&Wang王承 书1945)
基函数与经济波动的本质： 外来噪声驱动vs. 内生（非线性）振子 • 描写经济动力学的基函数 • 白噪声，谐振波，与 wavelets • Wigner transform, Gabor wavelet, and logistic wavelet • 经济波动 (business cycles) 的本质：内生震荡还是 外来噪声驱动？ • Frisch model of noise driven harmonic cycles (1933), Harmonically bounded Brownian motion (Unlenbeck & Orstein 1930, Unlenbeck & Wang 王承 书 1945)
噪声与混沌的模式识别 FSPCOM Filtered HP Cycles 0.3 0.2 + : 0.1 0.020.06 I) 0.3-0.2
噪声与混沌的模式识别 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 -0.3 X(t+T) -0.2 -0.1 0 0.1 0.2 0.3 X(t) FSPCOM Filtered HP Cycles
Math Representation in Frequency Domain Fourier spectrum e(f for color cycle and white noise
Math Representation in Frequency Domain • Fourier spectrum E(f) for color cycle and white noise
opectrum E(f of Harmonic Wave a S White Noise, and color Noise(Chaos Wa ave N oIse
Spectrum E(f) of Harmonic Wave, White Noise, and Color Noise (Chaos) • Wave Noise
Stationary (Discrete Fourier Transform)vs Non-Stationary (Joint-Time-Frequency analysis) Time Series Analysis钱世锷,陈大庞(1994 Application ofJoint Time-Frequency Analysis to /SAR DFTBSed ASAR J7Ae△ 4R lange ara Mc2
Stationary (Discrete Fourier Transform) vs. Non-Stationary (Joint-Time-Frequency Analysis) Time Series Analysis 钱世锷，陈大庞(1994)