Preamble

library("forecast")
library("fracdiff") # for fracdiff, fdGPH

Data

Raw Data

# US CPI, Jan 1947 - Jan 2017, Monthly
data <- read.csv("http://ptrckprry.com/course/forecasting/data/cpi.csv")
head(data)
        date   cpi
1 1947-01-01 21.48
2 1947-02-01 21.62
3 1947-03-01 22.00
4 1947-04-01 22.00
5 1947-05-01 21.95
6 1947-06-01 22.08
tail(data)
          date     cpi
836 2016-08-01 240.389
837 2016-09-01 241.006
838 2016-10-01 241.694
839 2016-11-01 242.199
840 2016-12-01 242.821
841 2017-01-01 244.158

Extract Variables

date <- as.Date(data$date)
cpi <- data$cpi
log.cpi <- log(cpi)
inflation <- c(NA, diff(log.cpi))

Average Inflation

Estimate

xbar <- mean(inflation, na.rm=TRUE)
print(xbar)
[1] 0.002893682

Standard Error (?)

n <- sum(!is.na(inflation))
s <- sd(inflation, na.rm=TRUE)
se <- s / sqrt(n)
print(se)
[1] 0.0001194141

95% Confidence Interval (?)

xbar + c(-1,1) * 1.96 * se
[1] 0.002659631 0.003127734

Time Series Plot

plot(date, inflation, type="l", col=2)

ACF, PACF

par(mfrow=c(1,2))
Acf(inflation, lag.max=200)
Pacf(inflation, lag.max=200)