时间序列预测,处理已知的大订单

Question

我有很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)

这个特定系列的前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)

有哪些方法可以预测考虑这些异常值的时间序列？

我已经尝试更换下一个最大的异常值(因此,运行数据集10次,用下一个最大值替换异常值,直到第10个数据集替换掉所有异常值).我也试过简单地删除异常值(因此每次再次运行数据集10次删除异常值,直到在第10个数据集中删除所有10个异常值)

我只想指出,删除这些大订单并不会完全删除数据点,因为该季度还会发生其他交易

我的代码通过多个预测模型测试数据(ARIMA加权样本,ARIMA加权样本,ARIMA加权,ARIMA,加性Holt-winters加权和Multiplcative Holt-winters加权)所以它需要是可以的适应这些多种模式.

以下是我使用的几个数据集,但我没有这些系列的异常值

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)

如果这太复杂了,那么在R中,如果使用某些命令检测到异常值,则如何处理数据以进行预测.例如平滑等以及我如何接近自己编写代码(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的功能.例如,最简单的模型可以对年份进行线性依赖,并对所有季节进行校正.代码看起来像:

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)

其结果如下图所示:

具有季节性调整但非依赖于年份的模型可以提供更好的拟合.