FRM数量分析

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

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①Independent / Strong White Noise：

serial：independent

②Gaussian / Normal White Noise：

serial：independent and normally distributed

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回归中常假设：disturbance是white noise

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displacement=0时：

①autocovariance = variance

②autocorrelation = 1

③partial autocorrelation = 1

displacement≠0时：

①autocovariance = 0

②autocorrelation = 0

③partial autocorrelation = 0

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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.

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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

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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 ＜ ∞