1. White Noise:(disturbance)
mean:0
variance:constant
serial:uncorrelated(无线性关系,有非线性关系)
autocorrelation = 0
autocovariance = 0
①Independent / Strong White Noise:
serial:independent
②Gaussian / Normal White Noise:
serial:independent and normally distributed
回归中常假设:disturbance是white noise
displacement=0时:
①autocovariance = variance
②autocorrelation = 1
③partial autocorrelation = 1
displacement≠0时:
①autocovariance = 0
②autocorrelation = 0
③partial autocorrelation = 0
unconditional mean and variance:constant
conditional and unconditional mean and variance:identical
No correlation between the past and the present of white noise series,no forecasting.
2. Lag Operator:L
Lyt = y(t-1)
L^(n)yt = y(t-n)
yt的变化量
= yt - y(t-1)
= yt - Lyt
=(1-L)yt
3. Wold Theorem:
任何一个协方差平稳的时间序列由无限个白噪声的滞后表达式构成
b0 = 1,
b0^2+b1^2 + b2^2 + b3^2 + … + bn^2 < ∞