On the basis of Figure 1, which plots the monthly rate of change in the seasonally adjusted CPI, realized inflation does indeed appear to be stationary, after taking a break in the mid 1990s into account. And in fact, a Phillips-Perron test rejects the I(1) hypothesis at the 1% level, while a KPSS test fails to reject the null of stationarity at any reasonable significance level for the two sample periods.