Nonlinear Time Series Analysis
Nonlinear Time Series Analysis
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DOI：
10.1007/978-3-642-04898-2_411
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发表时间：
2005-07
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影响因子：
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通讯作者：
H. Tong
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文献类型：
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作者：
H. Tong
在平稳时间序列分析中，谱密度函数即使存在，在上述定义下也是非线性的。然而，由于稍后将说明的原因，基于它或其等效的统计分析通常被认为是线性分析。通常，以离散的时间间隔观察时间序列。对于离散平稳时间序列1Xt: t=…，- 1,0,1，…l具有有限方差，corr （Xt, Xt+ s）是一个仅关于s的函数，比如ρ (s)，它被称为自相关函数。如果∑∞s=−∞| ρ (s)|< r，则谱密度函数是ρ (s)的傅里叶变换。现在，Yule（1927）引入了著名的时间序列自回归模型。该模型通常采用以下形式
In the analysis of stationary time series, the spectral density function, if it exists, is nonlinear under the above definition. However, for reasons to be made clear later, a statistical analysis that is based on it or its equivalents is ordinarily considered a linear analysis. Often, a time series is observed at discrete time intervals. For a discrete-time stationary time series 1Xt: t=...,-1, 0, 1,... l with finite variance, corr (Xt, Xt+ s) is a function of s only, say ρ (s), and is called the auto-correlation function. The spectral density function is the Fourier transform of ρ (s) if∑∞ s=−∞| ρ (s)|< с. Now, Yule (1927) introduced the celebrated autoregressive model in time series. Typically the model takes the form