Studying inflation dynamics using an ARDL model

inflation.R

library(tidyverse)

# CPI
# https://data.bls.gov/timeseries/CUSR0000SA0&output_view=pct_1mth
readxl::read_xlsx("~/Downloads/SeriesReport-20220817182003_bb0f80.xlsx", skip = 10) %>%
  mutate(date = seq.POSIXt(as.POSIXct("1957-02-01"), by = "month", length.out = n())) %>%
  select(date, cpi = Value) %>%
  inner_join(
    # Short-term Interest Rates - https://fred.stlouisfed.org/series/DGS1MO
    read_csv("~/Downloads/DGS1MO (1).csv", col_types = cols(
      DATE = col_date(format = ""),
      DGS1MO = col_number()
    )) %>%
      janitor::clean_names() %>%
      rename(treasury_1mo = dgs1mo) %>%
      # impute some missing values
      mutate(treasury_1mo = forecast::na.interp(treasury_1mo))) %>%
  mutate(cpi_annualized = (((1 + cpi/100)^12) - 1)*100, # annualize cpi
         # standardize on a 4% rate hike to aid interpretation
         treasury_1mo_std_on_4pct = treasury_1mo/4,
         lag_cpi_annualized = lag(cpi_annualized),
         lag_treasury_1mo_std_on_4pct = lag(treasury_1mo_std_on_4pct)) %>%
  arrange(date) %>%
  tail(36) -> cpi

# Both ~ I(1)
forecast::auto.arima(cpi$cpi_annualized)
forecast::auto.arima(cpi$treasury_1mo)


MASS::rlm(cpi_annualized ~ lag(cpi_annualized) +
            lag(treasury_1mo_std_on_4pct),
          data = cpi) -> fit

forecast::auto.arima(resid(fit))
plot(resid(fit), type = "b"); abline(h = 0, col = "red")
acf(resid(fit))
par(mfrow = c(2, 2)); plot(fit); par(mfrow = c(1, 1))
summary(fit)