吴同学2025-02-25 18:48:14
吴同学ACF与PACF如何理解他们之间的区别
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黄石2025-02-26 09:42:20
黄石同学你好。自相关系数描述 Yt 在任意两个不同时刻 t，t − h 的取值之间的相关程度。然而，该指标直接反映了 Yt 与 Yt−h 之间的相关关系，而没有控制中间 h − 1 个随机变量的变动。偏自相关系数则在将中间 h − 1 个随机变量看作已知的条件下研究 Yt 与 Yt−h 之间的相关关系，可通过 h 阶自回归拟合得到。见下图。
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根据AR和MA的公式，怎么理解与之相应的ACF,PACF的图像
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同学你好。
在AR模型中，对于时间序列的建模是将yt与其滞后项进行建模，故每期的yt都会包含此前的y的信息。这使得即便是yt与很久远的y之间也会存在关联，所以其ACF是缓慢衰减的拖尾形态。对于其PACF，根据定义，PACF是将yt与其滞后项跑回归得到的，如一阶partial autocorrelation指的是将yt对yt-1跑回归、得到的yt-1前面的系数；二阶partial autocorrelation指的是将yt对yt-1和yt-2跑回归、得到的yt-2前面的系数。显然，AR模型的PACF应是截尾的形态，比如如果数据服从AR (1)过程，那么在将yt对yt-1和yt-2跑回归时，得到的yt-2前面的系数理应在统计意义上不显著不等于0。
对于MA模型，结论与AR模型相反，反过来记忆即可。
180****86962025-02-27 11:06:47
ACF (Autocorrelation Function) and PACF (Partial Autocorrelation Function) are both tools used to analyze the relationships between time series data at different lags, but they measure different aspects. ACF shows the correlation between the time series and its own lagged values at various lags, capturing the overall dependency structure, including both direct and indirect relationships. It is useful for understanding the general pattern of autocorrelation in the data. PACF, on the other hand, measures the correlation between the time series and its lagged values after removing the effects of shorter lags. Essentially, it isolates the direct relationship between the series and its lags, without the influence of intermediate lags. The main difference between them is that ACF captures both direct and indirect dependencies, while PACF isolates only the direct dependency between a time series and its lagged values. PACF is often used to determine the order of AR models while ACF for MA.
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