如何从 ARIMA 模拟分布值以绘制为扇形图

Question

我有以下时间序列的 CPI 数据，我正在寻找创建一个扇形图（类似于 https://journal.r-project.org/archive/2015-1/abel.pdf 或 ggplot2 中的英格兰银行示例，如果可能的话）。

到目前为止，我已经根据我的时间序列创建了一个 ARIMA 模型。我正在寻找关于如何从我的模型中模拟随机变量分布并将其绘制为扇形图的解决方案。我希望为分布模拟提前 10 个周期。

这是我的数据集cpi的复制品

structure(list(Date = structure(c(1356998400, 1359676800, 1362096000, 
1364774400, 1367366400, 1370044800, 1372636800, 1375315200, 1377993600, 
1380585600, 1383264000, 1385856000, 1388534400, 1391212800, 1393632000, 
1396310400, 1398902400, 1401580800, 1404172800, 1406851200, 1409529600, 
1412121600, 1414800000, 1417392000, 1420070400, 1422748800, 1425168000, 
1427846400, 1430438400, 1433116800, 1435708800, 1438387200, 1441065600, 
1443657600, 1446336000, 1448928000, 1451606400, 1454284800, 1456790400, 
1459468800, 1462060800, 1464739200, 1467331200, 1470009600, 1472688000, 
1475280000, 1477958400, 1480550400, 1483228800, 1485907200, 1488326400, 
1491004800, 1493596800, 1496275200, 1498867200, 1501545600, 1504224000, 
1506816000, 1509494400, 1512086400, 1514764800, 1517443200, 1519862400, 
1522540800, 1525132800, 1527811200, 1530403200, 1533081600, 1535760000, 
1538352000, 1541030400, 1543622400, 1546300800, 1548979200, 1551398400, 
1554076800, 1556668800, 1559347200, 1561939200, 1564617600, 1567296000, 
1569888000, 1572566400, 1575158400, 1577836800, 1580515200, 1583020800, 
1585699200, 1588291200, 1590969600, 1593561600), class = c("POSIXct", 
"POSIXt"), tzone = "UTC"), CPI = c(100.943613610327, 101.355726290109, 
101.920519704091, 102.251765014058, 102.399483334481, 102.654230611209, 
103.366370423635, 103.771996583604, 104.069828647932, 104.475897454947, 
104.745585890252, 104.9, 105.877675706645, 106.600613244374, 
107.25658797107, 108.285287342243, 108.607710827378, 108.935592526775, 
109.11670321665, 109.390661099815, 109.563232156331, 109.694215435852, 
109.939646273932, 109.754097918499, 110.601049654351, 110.415206179718, 
110.905507883552, 111.45837834832, 111.873469766967, 112.253828314821, 
112.699336213665, 113.056054221625, 113.204653466884, 113.387164759728, 
113.581282843726, 113.810860009533, 116.506784014018, 117.199721025597, 
118.107968739773, 118.823678758349, 119.420709143437, 119.808600479962, 
120.575551335206, 120.774779709305, 121.014544917053, 121.61732414169, 
121.917354377998, 122.116542025261, 126.058371342546, 126.285551233707, 
126.43426615261, 126.763103151148, 126.92061331762, 127.095652703716, 
127.146439944094, 127.257270861715, 127.754395868046, 127.897364611267, 
128.227889139291, 128.426778898969, 130.540032633942, 130.730222134177, 
130.87769195147, 131.302356289165, 131.797387843531, 132.126557217198, 
132.823218725753, 132.868685232286, 133.870800057958, 134.439906096246, 
135.351580975176, 135.040382301698, 136.620612224767, 136.503608878263, 
136.763944144826, 137.24925661824, 137.169191683167, 137.331600194512, 
137.656945057261, 137.792027588476, 137.792027588476, 138.493686354623, 
138.681976535356, 138.535078801086, 139.421769773802, 139.848223614133, 
139.983926150073, 139.504431667605, 139.994961370897, 140.280481556844, 
140.529583177439)), row.names = c(NA, -91L), class = c("tbl_df", 
"tbl", "data.frame"))

这是到目前为止我的模型的代码

# Load Packages
library(pacman)
pacman::p_load(tseries, tidyverse, urca, forecast, tbl2xts)


# Create a log transformation for CPI and convert from tibble to time series format

cpi.ts <- cpi %>% 
  mutate(CPI = log(CPI)) %>% 
  tbl_xts()

# Test for a unit root using an ADF test

adf.cpi.ts <- ur.df(cpi.ts, type = "none", selectlags = "AIC")
summary(adf.cpi.ts)

# Create an ARIMA Model using cpi.ts

arima <- auto.arima(cpi.ts)

这是arima的结果

ARIMA(0,1,0) with drift 

Coefficients:
       drift
      0.0037
s.e.  0.0005

sigma^2 estimated as 2.255e-05:  log likelihood=354.77
AIC=-705.54   AICc=-705.4   BIC=-700.54

我可以使用arima.sim 函数来执行此操作吗（如果可以，我该如何执行此操作？）。理想情况下，我正在寻找类似于下图的最终解决方案（如果我能找到 ggplot2 解决方案会更好。

TIA

Answer 1

这里有两个问题 - 如何从模型中模拟未来值，以及如何将预测（或模拟）绘制为扇形图。两者都可以使用 fable 包完成。

library(tidyverse)
library(tsibble)
library(fable)

# Create tsibble object
cpi <- cpi %>% 
  mutate(Date = yearmonth(Date)) %>%
  as_tsibble(index=Date)

# Fit ARIMA model to log data
fit <- cpi %>%
  model(arima = ARIMA(log(CPI)))

# Simulated future sample paths
fit %>%
  generate(times=20, h="1 year") %>%
  autoplot(.sim) + autolayer(cpi, CPI) +
  ylab("CPI") +
  theme(legend.position="none")

# Fan plot
fit %>%
  forecast(h="1 year") %>%
  autoplot(cpi, level=seq(10,90,by=10)) +
  theme(legend.position="none")

^{由reprex package (v0.3.0) 于 2020-08-19 创建}