Forecasting Inflation, 2022
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#install.packages("quantmod")
#install.packages("forecast")Load data
The CPI data is available at the St. Louis Federal Reserve. We can load the data directly into R.
library(quantmod)## Loading required package: xts## Loading required package: zoo##
## Attaching package: 'zoo'## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numeric## Loading required package: TTR## Registered S3 method overwritten by 'quantmod':
## method from
## as.zoo.data.frame zoocpi<-getSymbols(Symbols = "CPILFESL",src="FRED",auto.assign=FALSE)
cpi$dCPI<-Delt(cpi[,1],k=12,type="log")
cpi$LdCPI<-Lag(cpi$dCPI,k=12)Summary statistics
print(summary(cpi))## Index CPILFESL dCPI LdCPI
## Min. :1957-01-01 Min. : 28.50 Min. :0.006009 Min. :0.006009
## 1st Qu.:1974-01-08 1st Qu.: 46.98 1st Qu.:0.019868 1st Qu.:0.019784
## Median :1991-01-16 Median :139.85 Median :0.027466 Median :0.026882
## Mean :1991-01-15 Mean :139.79 Mean :0.035813 Mean :0.035857
## 3rd Qu.:2008-01-24 3rd Qu.:213.90 3rd Qu.:0.045260 3rd Qu.:0.045911
## Max. :2025-02-01 Max. :325.48 Max. :0.127553 Max. :0.127553
## NA's :12 NA's :24plot(cpi$dCPI,main="Proportional change in CPI")
Modeling inflation
How well does the model forecast for the November, 2018 to October, 2019 time period?
library(forecast)
inflation_model19<-auto.arima(y=cpi$dCPI[index(cpi)<as.Date("2018-11-01")])
print(inflation_model19)## Series: cpi$dCPI[index(cpi) < as.Date("2018-11-01")]
## ARIMA(1,1,3)
##
## Coefficients:
## ar1 ma1 ma2 ma3
## 0.8339 -0.6510 0.1144 -0.1199
## s.e. 0.0614 0.0721 0.0462 0.0457
##
## sigma^2 = 5.146e-06: log likelihood = 3406.09
## AIC=-6802.19 AICc=-6802.1 BIC=-6779.23window19<-seq(as.Date("2018-11-01"),length=12,by="1 months")
cpi$f19_dCPI_LB<-NA
cpi$f19_dCPI_UB<-NA
cpi$f19_dCPI_MN<-NA
cpi$f19_dCPI_LB[window19]<-as.numeric(forecast(inflation_model19,h=12)[["lower"]][,1])
cpi$f19_dCPI_UB[window19]<-as.numeric(forecast(inflation_model19,h=12)[["upper"]][,1])
cpi$f19_dCPI_MN[window19]<-as.numeric(forecast(inflation_model19,h=12)[["mean"]])
plot(cpi[window19,c(2,4,5,6)],
main="Inflation: Nov 2018 - Oct 2019",
ylim=range(na.omit(c(as.numeric(cpi$dCPI[window19]),
as.numeric(cpi$f19_dCPI_LB[window19]),
as.numeric(cpi$f19_dCPI_UB[window19])))))
How well does the model forecast from November, 2019 to October, 2020 time period?
inflation_model20<-auto.arima(y=cpi$dCPI[index(cpi)<as.Date("2019-11-01")])
print(inflation_model20)## Series: cpi$dCPI[index(cpi) < as.Date("2019-11-01")]
## ARIMA(1,1,3)
##
## Coefficients:
## ar1 ma1 ma2 ma3
## 0.8337 -0.6507 0.1147 -0.1205
## s.e. 0.0612 0.0718 0.0458 0.0453
##
## sigma^2 = 5.072e-06: log likelihood = 3467.5
## AIC=-6924.99 AICc=-6924.91 BIC=-6901.95window20<-seq(as.Date("2019-11-01"),length=12,by="1 months")
cpi$f20_dCPI_LB<-NA
cpi$f20_dCPI_UB<-NA
cpi$f20_dCPI_MN<-NA
cpi$f20_dCPI_LB[window20]<-as.numeric(forecast(inflation_model20,h=12)[["lower"]][,1])
cpi$f20_dCPI_UB[window20]<-as.numeric(forecast(inflation_model20,h=12)[["upper"]][,1])
cpi$f20_dCPI_MN[window20]<-as.numeric(forecast(inflation_model20,h=12)[["mean"]])
plot(cpi[window20,c(2,7,8,9)],
main="Inflation: Nov 2019 - Oct 2020",
ylim=range(na.omit(c(as.numeric(cpi$dCPI[window20]),
as.numeric(cpi$f20_dCPI_LB[window20]),
as.numeric(cpi$f20_dCPI_UB[window20])))))
How well does the model forecast from November, 2020 to October, 2021 time period?
inflation_model21<-auto.arima(y=cpi$dCPI[index(cpi)<as.Date("2020-11-01")])
print(inflation_model21)## Series: cpi$dCPI[index(cpi) < as.Date("2020-11-01")]
## ARIMA(1,1,3) with drift
##
## Coefficients:
## ar1 ma1 ma2 ma3 drift
## 0.8340 -0.6435 0.1056 -0.1240 0e+00
## s.e. 0.0626 0.0728 0.0456 0.0453 2e-04
##
## sigma^2 = 5.095e-06: log likelihood = 3522.46
## AIC=-7032.92 AICc=-7032.81 BIC=-7005.18window21<-seq(as.Date("2020-11-01"),length=12,by="1 months")
cpi$f21_dCPI_LB<-NA
cpi$f21_dCPI_UB<-NA
cpi$f21_dCPI_MN<-NA
cpi$f21_dCPI_LB[window21]<-as.numeric(forecast(inflation_model21,h=12)[["lower"]][,1])
cpi$f21_dCPI_UB[window21]<-as.numeric(forecast(inflation_model21,h=12)[["upper"]][,1])
cpi$f21_dCPI_MN[window21]<-as.numeric(forecast(inflation_model21,h=12)[["mean"]])
plot(cpi[window21,c(2,10,11,12)],
main="Inflation: Nov 2020 - Oct 2021",
ylim=range(na.omit(c(as.numeric(cpi$dCPI[window21]),
as.numeric(cpi$f21_dCPI_LB[window21]),
as.numeric(cpi$f21_dCPI_UB[window21])))))
How well does the model forecast from November, 2021 to October, 2022 time period?
inflation_model22<-auto.arima(y=cpi$dCPI[index(cpi)<as.Date("2021-11-01")])
print(inflation_model22)## Series: cpi$dCPI[index(cpi) < as.Date("2021-11-01")]
## ARIMA(2,1,3)
##
## Coefficients:
## ar1 ar2 ma1 ma2 ma3
## 0.8114 0.0261 -0.5895 0.0654 -0.1460
## s.e. 0.1819 0.1367 0.1783 0.1052 0.0458
##
## sigma^2 = 5.366e-06: log likelihood = 3558.75
## AIC=-7105.5 AICc=-7105.39 BIC=-7077.66window22<-seq(as.Date("2021-11-01"),length=12,by="1 months")
cpi$f22_dCPI_LB<-NA
cpi$f22_dCPI_UB<-NA
cpi$f22_dCPI_MN<-NA
cpi$f22_dCPI_LB[window22]<-as.numeric(forecast(inflation_model22,h=12)[["lower"]][,1])
cpi$f22_dCPI_UB[window22]<-as.numeric(forecast(inflation_model22,h=12)[["upper"]][,1])
cpi$f22_dCPI_MN[window22]<-as.numeric(forecast(inflation_model22,h=12)[["mean"]])
plot(cpi[window22,c(2,13,14,15)],
main="Inflation: Nov 2021 - Oct 2022",
ylim=range(na.omit(c(as.numeric(cpi$dCPI[window22]),
as.numeric(cpi$f22_dCPI_LB[window22]),
as.numeric(cpi$f22_dCPI_UB[window22])))))
How well does the model forecast from November, 2022 to October, 2023 time period?
inflation_model23<-auto.arima(y=cpi$dCPI[index(cpi)<as.Date("2022-11-01")])
print(inflation_model23)## Series: cpi$dCPI[index(cpi) < as.Date("2022-11-01")]
## ARIMA(0,1,3)
##
## Coefficients:
## ma1 ma2 ma3
## 0.2444 0.2737 0.0668
## s.e. 0.0365 0.0379 0.0335
##
## sigma^2 = 5.419e-06: log likelihood = 3609.67
## AIC=-7211.34 AICc=-7211.29 BIC=-7192.72window23<-seq(as.Date("2022-11-01"),length=12,by="1 months")
cpi$f23_dCPI_LB<-NA
cpi$f23_dCPI_UB<-NA
cpi$f23_dCPI_MN<-NA
cpi$f23_dCPI_LB[window23]<-as.numeric(forecast(inflation_model23,h=12)[["lower"]][,1])
cpi$f23_dCPI_UB[window23]<-as.numeric(forecast(inflation_model23,h=12)[["upper"]][,1])
cpi$f23_dCPI_MN[window23]<-as.numeric(forecast(inflation_model23,h=12)[["mean"]])
plot(cpi[window23,c(2,16,17,18)],
main="Inflation: Nov 2022 - Oct 2023",
ylim=range(na.omit(c(as.numeric(cpi$dCPI[window23]),
as.numeric(cpi$f23_dCPI_LB[window23]),
as.numeric(cpi$f23_dCPI_UB[window23])))))
How well does the model forecast from November, 2023 to October, 2024 time period?
inflation_model24<-auto.arima(y=cpi$dCPI[index(cpi)<as.Date("2023-11-01")])
print(inflation_model24)## Series: cpi$dCPI[index(cpi) < as.Date("2023-11-01")]
## ARIMA(0,1,3) with drift
##
## Coefficients:
## ma1 ma2 ma3 drift
## 0.2508 0.2769 0.0685 0e+00
## s.e. 0.0361 0.0375 0.0333 1e-04
##
## sigma^2 = 5.388e-06: log likelihood = 3668.21
## AIC=-7326.43 AICc=-7326.35 BIC=-7303.07window24<-seq(as.Date("2023-11-01"),length=12,by="1 months")
cpi$f24_dCPI_LB<-NA
cpi$f24_dCPI_UB<-NA
cpi$f24_dCPI_MN<-NA
cpi$f24_dCPI_LB[window24]<-as.numeric(forecast(inflation_model24,h=12)[["lower"]][,1])
cpi$f24_dCPI_UB[window24]<-as.numeric(forecast(inflation_model24,h=12)[["upper"]][,1])
cpi$f24_dCPI_MN[window24]<-as.numeric(forecast(inflation_model24,h=12)[["mean"]])
plot(cpi[window24,c(2,19,20,21)],
main="Inflation: Nov 2023 - Oct 2024",
ylim=range(na.omit(c(as.numeric(cpi$dCPI[window24]),
as.numeric(cpi$f24_dCPI_LB[window24]),
as.numeric(cpi$f24_dCPI_UB[window24])))))
Forecasting for the next year
inflation_model25<-auto.arima(y=cpi$dCPI[index(cpi)<as.Date("2024-11-01")])
print(inflation_model25)## Series: cpi$dCPI[index(cpi) < as.Date("2024-11-01")]
## ARIMA(0,1,3)
##
## Coefficients:
## ma1 ma2 ma3
## 0.2513 0.2763 0.0682
## s.e. 0.0358 0.0371 0.0330
##
## sigma^2 = 5.313e-06: log likelihood = 3729.05
## AIC=-7450.1 AICc=-7450.05 BIC=-7431.36window25<-seq(as.Date("2024-11-01"),length=12,by="1 months")
f25_dCPI_LB<-as.numeric(forecast(inflation_model25,h=12)[["lower"]][,1])
f25_dCPI_UB<-as.numeric(forecast(inflation_model25,h=12)[["upper"]][,1])
f25_dCPI_MN<-as.numeric(forecast(inflation_model25,h=12)[["mean"]])
cpiF<-xts(x=data.frame(f25_dCPI_LB,f25_dCPI_UB,f25_dCPI_MN),order.by=window25)
plot(cpiF[window25,],
main="Inflation: Nov 2024 - Oct 2025",
ylim=range(na.omit(c(as.numeric(cpiF$f25_dCPI_LB[window25]),
as.numeric(cpiF$f25_dCPI_UB[window25])))))