在 ggplot2 中为绘制的 ACF 添加置信区间

问题描述

我计划为模拟时间序列构建自定义 ACF 和 PACF 图

ts 

以下是我编写的通过 ggplot2 生成绘图的代码:

库(gridExtra)主题设置 <- 主题(panel.background = element_blank(),panel.grid.major.y = element_line(color="grey90", size=0.5),panel.grid.major.x = element_blank(),panel.border = element_rect(fill=NA, color="grey20"),axis.text = element_text(family="Times"),axis.title = element_text(family="Times"),plot.title = element_text(size=10, hjust=0.5, family="Times"))acf_ver_conf <- acf(ts, plot=FALSE)$acf %>%as_tibble() %>% 变异(滞后 = 1:n()) %>%ggplot(aes(x=lags, y = V1)) + scale_x_continuous(breaks=seq(0,41,4)) +实验室(y =自相关"，x =滞后"，标题=时间序列，ACF")+geom_segment(aes(xend=lags，yend=0))+geom_point()+主题设置pacf_ver_conf <- pacf(ts, main=NULL,plot=FALSE)$acf %>%as_tibble() %>% 变异(滞后 = 1:n()) %>%ggplot(aes(x=lags, y = V1)) +geom_segment(aes(xend=lags，yend=0)) +geom_point() + theme_setting +scale_x_continuous(breaks=seq(0,41,4))+实验室(y =偏自相关"，x =滞后"，标题=时间序列，PACF")grid.arrange(acf_ver_conf, pacf_ver_conf, ncol=2)

虽然这正是我想要的，但我不确定如何在 acf(ts) 和 pacf(ts) 中生成置信区间:

所以，我的问题分为两部分:

• 如何从统计上推导出 R 中自相关函数和偏自相关的置信区间的上限和下限?
• 如何将其绘制到第一张图上?我在考虑 geom_ribbon，但如果有任何其他想法，我们将不胜感激！

解决方案

这可能有效(置信限的公式取自这里

alpha 

ts.pacf <- pacf(ts, main=NULL,plot=TRUE)

alpha 

I plan to build a customized ACF and PACF plot for a simulated time series

ts <- arima.sim(n=5300,list(order=c(2,0,1), ar=c(0.4,0.3), ma=-0.2))

Below are the codes I wrote to produce the plot through ggplot2:

library(gridExtra)
theme_setting <- theme(
  panel.background = element_blank(),
  panel.grid.major.y = element_line(color="grey90", size=0.5),
  panel.grid.major.x = element_blank(),
  panel.border = element_rect(fill=NA, color="grey20"),
  axis.text = element_text(family="Times"),
  axis.title = element_text(family="Times"),
  plot.title = element_text(size=10, hjust=0.5, family="Times"))

acf_ver_conf <- acf(ts, plot=FALSE)$acf %>%
  as_tibble() %>% mutate(lags = 1:n()) %>%
  ggplot(aes(x=lags, y = V1)) + scale_x_continuous(breaks=seq(0,41,4)) +
  labs(y="Autocorrelations", x="Lag", title= "Time Series, ACF") +
  geom_segment(aes(xend=lags, yend=0)) +geom_point() + theme_setting

pacf_ver_conf <- pacf(ts, main=NULL,plot=FALSE)$acf %>%
  as_tibble() %>% mutate(lags = 1:n()) %>%
  ggplot(aes(x=lags, y = V1)) +
  geom_segment(aes(xend=lags, yend=0)) +geom_point() + theme_setting +
  scale_x_continuous(breaks=seq(0,41,4))+
  labs(y="Partial Autocorrelations", x="Lag", title= "Time Series, PACF")

grid.arrange(acf_ver_conf, pacf_ver_conf, ncol=2)

While this is exactly what I want, I am not sure how to produce the confidence intervals in acf(ts) and pacf(ts):

So, my question has two parts:

• How to statistically derive the upper and lower bound of the confidence intervals for Autocorrelated Functions and Partial Autocorrelations in R?
• How would you plot it onto the first graph? I was thinking about geom_ribbon but any additional idea will be appreciated!

解决方案

This may work (the formula for the confidence limits are taken from here https://stats.stackexchange.com/questions/211628/how-is-the-confidence-interval-calculated-for-the-acf-function, may need some tweaking):

ts.acf <- acf(ts, plot=TRUE)

alpha <- 0.95
conf.lims <- c(-1,1)*qnorm((1 + alpha)/2)/sqrt(ts.acf$n.used)

ts.acf$acf %>%
  as_tibble() %>% mutate(lags = 1:n()) %>%
  ggplot(aes(x=lags, y = V1)) + scale_x_continuous(breaks=seq(0,41,4)) +
  geom_hline(yintercept=conf.lims, lty=2, col='blue') +
  labs(y="Autocorrelations", x="Lag", title= "Time Series, ACF") +
  geom_segment(aes(xend=lags, yend=0)) +geom_point() + theme_setting

ts.pacf <- pacf(ts, main=NULL,plot=TRUE)

alpha <- 0.95
conf.lims <- c(-1,1)*qnorm((1 + alpha)/2)/sqrt(ts.pacf$n.used)

ts.pacf$acf %>%
  as_tibble() %>% mutate(lags = 1:n()) %>%
  ggplot(aes(x=lags, y = V1)) +
  geom_segment(aes(xend=lags, yend=0)) +geom_point() + theme_setting +
  scale_x_continuous(breaks=seq(0,41,4))+
  geom_hline(yintercept=conf.lims, lty=2, col='blue') +
  labs(y="Partial Autocorrelations", x="Lag", title= "Time Series, PACF")

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