r - 时间序列预测，处理已知的大订单

Question

我有许多已知异常值的数据集(大订单)

data <- matrix(c("08Q1","08Q2","08Q3","08Q4","09Q1","09Q2","09Q3","09Q4","10Q1","10Q2","10Q3","10Q4","11Q1","11Q2","11Q3","11Q4","12Q1","12Q2","12Q3","12Q4","13Q1","13Q2","13Q3","13Q4","14Q1","14Q2","14Q3","14Q4","15Q1", 155782698, 159463653.4, 172741125.6, 204547180, 126049319.8, 138648461.5, 135678842.1, 242568446.1, 177019289.3, 200397120.6, 182516217.1, 306143365.6, 222890269.2, 239062450.2, 229124263.2, 370575384.7, 257757410.5, 256125841.6, 231879306.6, 419580274, 268211059, 276378232.1, 261739468.7, 429127062.8, 254776725.6, 329429882.8, 264012891.6, 496745973.9, 284484362.55),ncol=2,byrow=FALSE)

该特定系列的前11个异常值是:

outliers <- matrix(c("14Q4","14Q2","12Q1","13Q1","14Q2","11Q1","11Q4","14Q2","13Q4","14Q4","13Q1",20193525.68, 18319234.7, 12896323.62, 12718744.01, 12353002.09, 11936190.13, 11356476.28, 11351192.31, 10101527.85, 9723641.25, 9643214.018),ncol=2,byrow=FALSE)

考虑到这些离群值，我可以使用哪些方法来预测时间序列？

我已经尝试替换下一个最大的离群值(因此，将数据集运行10次，用第二个最大的离群值替换，直到第10个数据集替换了所有离群值为止)。
我也尝试过简单地删除异常值(因此再次运行数据集10次，每次删除一个异常值，直到在第10个数据集中删除所有10个值为止)

我只想指出，删除这些大订单并不能完全删除数据点，因为该季度还有其他交易发生

我的代码通过多个预测模型(ARIMA加权在外样本上，ARIMA加权在内样本上，ARIMA加权，ARIMA，加性霍尔特冬天加权和多能霍尔特冬天加权)测试数据。因此，它必须是可以适应这些多种模型。

这是我使用的更多数据集，但是我没有这些系列的离群值

data <- matrix(c("08Q1","08Q2","08Q3","08Q4","09Q1","09Q2","09Q3","09Q4","10Q1","10Q2","10Q3","10Q4","11Q1","11Q2","11Q3","11Q4","12Q1","12Q2","12Q3","12Q4","13Q1","13Q2","13Q3","13Q4","14Q1","14Q2","14Q3", 26393.99306, 13820.5037, 23115.82432,    25894.41036,    14926.12574,    15855.8857, 21565.19002,    49373.89675,    27629.10141,    43248.9778, 34231.73851,    83379.26027,    54883.33752,    62863.47728,    47215.92508,    107819.9903,    53239.10602,    71853.5,    59912.7624, 168416.2995,    64565.6211, 94698.38748,    80229.9716, 169205.0023,    70485.55409,    133196.032, 78106.02227), ncol=2,byrow=FALSE)

data <- matrix(c("08Q1","08Q2","08Q3","08Q4","09Q1","09Q2","09Q3","09Q4","10Q1","10Q2","10Q3","10Q4","11Q1","11Q2","11Q3","11Q4","12Q1","12Q2","12Q3","12Q4","13Q1","13Q2","13Q3","13Q4","14Q1","14Q2","14Q3",3311.5124,    3459.15634, 2721.486863,    3286.51708, 3087.234059,    2873.810071,    2803.969394,    4336.4792,  4722.894582,    4382.349583,    3668.105825,    4410.45429, 4249.507839,    3861.148928,    3842.57616, 5223.671347,    5969.066896,    4814.551389,    3907.677816,    4944.283864,    4750.734617,    4440.221993,    3580.866991,    3942.253996,    3409.597269,    3615.729974,    3174.395507),ncol=2,byrow=FALSE)

如果这太复杂，则说明如何在R中使用某些命令检测到异常值后如何处理数据以进行预测。例如平滑等，以及我如何自己编写代码(不使用检测异常值的命令)

Answer 1

您的异常值似乎是季节性变化，最大的订单出现在第4季度。您提到的许多预测模型都包含季节性调整功能。例如，最简单的模型可能对年份具有线性依赖性，并且对所有季节进行校正。代码如下所示:

df <- data.frame(period= c("08Q1","08Q2","08Q3","08Q4","09Q1","09Q2","09Q3","09Q4","10Q1","10Q2","10Q3",
                       "10Q4","11Q1","11Q2","11Q3","11Q4","12Q1","12Q2","12Q3","12Q4","13Q1","13Q2",
                       "13Q3","13Q4","14Q1","14Q2","14Q3","14Q4","15Q1"),
                 order= c(155782698, 159463653.4, 172741125.6, 204547180, 126049319.8, 138648461.5,
                        135678842.1, 242568446.1, 177019289.3, 200397120.6, 182516217.1, 306143365.6,
                        222890269.2, 239062450.2, 229124263.2, 370575384.7, 257757410.5, 256125841.6,
                        231879306.6, 419580274, 268211059, 276378232.1, 261739468.7, 429127062.8, 254776725.6,
                        329429882.8, 264012891.6, 496745973.9, 42748656.73))

seasonal <- data.frame(year=as.numeric(substr(df$period, 1,2)), qtr=substr(df$period, 3,4), data=df$order)
ord_model <- lm(data ~ year + qtr, data=seasonal)
seasonal <- cbind(seasonal, fitted=ord_model$fitted)
library(reshape2)
library(ggplot2)
plot_fit <- melt(seasonal,id.vars=c("year", "qtr"), variable.name = "Source", value.name="Order" )
ggplot(plot_fit, aes(x=year, y = Order, colour = qtr, shape=Source)) + geom_point(size=3)

给出的结果如下表所示:


具有季节性调整但对年份的非线性依赖关系的模型可能会更好地拟合。