How to simulate distribution values from an ARIMA in order to plot as a fanchart

Question

I have the following time series of CPI data, which I am looking to create a fanchart (similar to the Bank of England Example in https://journal.r-project.org/archive/2015-1/abel.pdf , or in ggplot2 if that is possible).

So far, I have created an ARIMA model from my time series. I am looking for a solution on how to simulate a distribution of random variables from my model and plot it as a fanchart. I am looking to simulate 10 periods ahead for the distribution.

Here is a reproductible of my dataset cpi

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"))

Here is the code for my model so far

# 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)

and here are the results for arima

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

Could I go about doing this using the arima.sim function (and if yes, how could I go about doing it?). Ideally, I'm looking for my end solution to look something like the graph below (it would be even better if I could find a ggplot2 solution though.

TIA

Answer 1

There are two questions here -- how to simulate future values from the model, and how to plot the forecasts (or simulations) as a fan chart. Both can be done using the fable package.

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")

^{Created on 2020-08-19 by the reprex package (v0.3.0)}