用 ACF 和 PACF 解釋季節性

我有一個數據集，經驗直覺說我應該期待每週的季節性（即，週六和周日的行為與一周的其他時間不同）。如果這個前提是真的，自相關圖不應該讓我以 7 的滯後倍數爆發嗎？

以下是數據示例：

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}}]

…和ACF：

…和PACF：

首先，這是您的直覺，以簡化的時間序列說明，其中周末在 ACF 中很明顯：

但是，當數據具有某種趨勢時，可以掩蓋這種預期的 ACF 模式：

一個解決方案（如果這是一個問題）是在確定季節性時估計和控制趨勢。

生成這些圖的 R 代碼如下：

# 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))

引用自：https://stats.stackexchange.com/questions/45191