用ACF和PACF解释季节性

我有一个数据集，凭经验凭直觉说我应该期望每周都有季节性（即星期六和星期日的行为不同于一周的其余时间）。这个前提是否正确，自相关图是否应该让我以7的倍数倍数出现猝发？

这是数据示例：

data = TemporalData[{{{2012, 09, 28}, 19160768}, {{2012, 09, 19}, 
    19607936}, {{2012, 09, 08}, 7867456}, {{2012, 09, 15}, 
    11245024}, {{2012, 09, 04}, 0}, {{2012, 09, 21}, 
    24314496}, {{2012, 09, 12}, 11233632}, {{2012, 09, 03}, 
    9886496}, {{2012, 09, 09}, 9122272}, {{2012, 09, 24}, 
    23103456}, {{2012, 09, 20}, 25721472}, {{2012, 09, 11}, 
    12272160}, {{2012, 09, 25}, 21876960}, {{2012, 09, 05}, 
    7182528}, {{2012, 09, 16}, 11754752}, {{2012, 09, 23}, 
    23737248}, {{2012, 09, 26}, 20985984}, {{2012, 09, 10}, 
    12123584}, {{2012, 09, 06}, 9076736}, {{2012, 09, 17}, 
    20123328}, {{2012, 09, 18}, 20634720}, {{2012, 09, 22}, 
    23361024}, {{2012, 09, 14}, 11804928}, {{2012, 09, 07}, 
    9007200}, {{2012, 09, 02}, 9244192}, {{2012, 09, 13}, 
    11335328}, {{2012, 09, 27}, 20694720}, {{2012, 10, 26}, 
    12242112}, {{2012, 10, 15}, 10963776}, {{2012, 11, 09}, 
    9735424}, {{2012, 10, 08}, 10078240}, {{2012, 10, 31}, 
    10676736}, {{2012, 10, 20}, 11719840}, {{2012, 11, 05}, 
    10475168}, {{2012, 10, 01}, 9988416}, {{2012, 10, 24}, 
    11998688}, {{2012, 10, 12}, 10393120}, {{2012, 10, 23}, 
    11987936}, {{2012, 10, 19}, 11165536}, {{2012, 10, 04}, 
    9902720}, {{2012, 11, 16}, 10023648}, {{2012, 11, 21}, 
    10047936}, {{2012, 10, 10}, 10205568}, {{2012, 11, 08}, 
    9872832}, {{2012, 10, 21}, 12854112}, {{2012, 11, 04}, 
    10485856}, {{2012, 10, 07}, 9565248}, {{2012, 09, 30}, 
    9784864}, {{2012, 10, 29}, 12880064}, {{2012, 11, 10}, 
    8945824}, {{2012, 11, 15}, 9870880}, {{2012, 09, 29}, 
    9718080}, {{2012, 10, 18}, 10992896}, {{2012, 10, 06}, 
    9319584}, {{2012, 11, 03}, 9077024}, {{2012, 10, 03}, 
    10537408}, {{2012, 11, 22}, 9853216}, {{2012, 10, 11}, 
    10191936}, {{2012, 10, 22}, 12766816}, {{2012, 11, 07}, 
    9510624}, {{2012, 11, 14}, 9707264}, {{2012, 10, 28}, 
    12060736}, {{2012, 11, 19}, 10946880}, {{2012, 11, 11}, 
    9529568}, {{2012, 10, 09}, 9967680}, {{2012, 10, 17}, 
    12093344}, {{2012, 11, 20}, 10520800}, {{2012, 10, 05}, 
    9619136}, {{2012, 10, 25}, 11484288}, {{2012, 11, 17}, 
    9389312}, {{2012, 10, 30}, 12078944}, {{2012, 10, 14}, 
    9505984}, {{2012, 10, 02}, 9943648}, {{2012, 11, 24}, 
    9458144}, {{2012, 11, 02}, 10082944}, {{2012, 11, 01}, 
    11082912}, {{2012, 10, 13}, 9117632}, {{2012, 11, 23}, 
    10253280}, {{2012, 11, 12}, 10240672}, {{2012, 11, 06}, 
    9723456}, {{2012, 11, 13}, 9806880}, {{2012, 10, 16}, 
    12368896}, {{2012, 11, 18}, 9632800}, {{2012, 10, 27}, 10606656}}]

...以及ACF：

...以及PACF：

首先，这是在简化的时间序列中说明的直觉，其中周末在ACF中很明显：

但是，当数据有某种趋势时，可以屏蔽此预期的ACF模式：

一个解决方案（如果有问题）是在确定季节性时估计和控制趋势。

产生这些图的R代码如下：

# fourteen repeating 'weeks' of five zeroes and two ones
weekendeffect <- rep(c(rep(0,5),1,1),times=14)

plot(weekendeffect,
    main="Weekly pattern of five zeroes & two ones",
    xlab="Time", ylab="Value")  
acf(weekendeffect, main="ACF")

# add steady trend 
dailydrift <- 0.05
drift <- seq(from=dailydrift, to=length(weekendeffect)*dailydrift, 
   by=dailydrift)
driftingtimeseries <- drift + weekendeffect 

plot(driftingtimeseries,
    main=c("Weekly pattern with daily drift of",dailydrift),
    xlab="Time", ylab="Value")  
acf(driftingtimeseries, main=c("ACF with daily drift of",dailydrift))


# add larger trend 
dailydrift <- 0.1
drift <- seq(from=dailydrift, to=length(weekendeffect)*dailydrift, 
   by=dailydrift)
driftingtimeseries <- drift + weekendeffect 

plot(driftingtimeseries,
    main=c("Weekly pattern with daily drift of",dailydrift),
    xlab="Time", ylab="value")  
acf(driftingtimeseries, main=c("ACF with daily drift of",dailydrift))

您是否使用差分技术使数据保持平稳？您的ACF图表明您可能尚未完成此步骤。一旦有了平稳序列，就可以更轻松地解释图。我添加了两个大学资源，可以帮助您进行区分和解释。

宾夕法尼亚州立大学

杜克大学