序列相关性分析——总结
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该文章属于“时间序列分析”系列文章，是之前在校阶段的学习总结。为避免翻译歧义，采用英文写作。当前主题分为三个部分，自协方差、自相关函数、偏自相关函数。
前面文章说了自协方差、自相关函数(ACF)、偏自相关函数（PACF）,这篇文章做一个简单总结。另外引出了 ARMA 这个模型，作为时间序列分析模型的概念引出，它算是 ACF 和 PACF 的一个应用。在后面的文章中会继续介绍这个模型。
In time series analysis, we should always focus on the correlation itself. Because there exists no other series to compare, we define autocovariance, autocorrelation function and partial autocorrelation function based on the characteristics of the time series.
Word auto means we do the analysis on itself.
Summary
Autocovariance = Covariance
Autocorrelation = Pearson correaltion coefficient calculated with the expectation of the whole process
Partial Autocorrelation = Pearson correaltion coefficient calculated with the expectations respectively
ARMA
| Process | ACF | PACF |
|---|---|---|
| AR($p$) | Tails off gradually | Cuts off after $p$ lags |
| MA($q$) | Cuts off after $q$ lags | Tails off gradually |
| ARMA($p, q$) | Tails off gradually | Tails off gradually |