Examining US CPI persistence by using using the fractional-differencing technique of time series analysis. In this analysis, I roll the differencing procedure over a 120 month window to expose changes in the underlying process of inflation persistence.

gistfile1.txt

library(tidyverse)

# CPI
# https://data.bls.gov/timeseries/CUSR0000SA0&output_view=pct_1mth
readxl::read_xlsx("~/Downloads/SeriesReport-20220807120638_733b06.xlsx", skip = 10) %>%
  mutate(date = seq.POSIXt(as.POSIXct("1947-02-01"), by = "month", length.out = n())) %>%
  select(date, cpi = Value) -> cpi

cpi %>%
  filter(date >= as.POSIXct("1949-01-01")) %>%
  mutate(frac_d = zoo::rollapplyr(cpi, width = 120, fill = NA, function(x) {
    fracdiff::fracdiff(x, nar = 1)[["d"]] # rolling fractionally-differened ARIMA
  })) %>%
  ggplot(aes(date, frac_d)) +
  geom_line() + geom_point() +
  ggtitle("US CPI persistence over time (rolling order of integration)") +
  labs(y = "Fractional d", x = "") +
  scale_x_datetime(date_breaks = "5 year", date_labels = "%Y") +
  theme_bw(25) +
  theme(panel.grid.minor = element_blank())