# Understanding stationarity with Inflation

I am looking at the link between inflation and insolvencies for an econometrics project. I have the raw quarterly insolvency data and raw quarterly CPI data for the UK (roughly 100 samples) from 1988-2013.

Both of these are non-stationary at the 5%, and both are I(1) on checking the raw data. I am using 5% levels for all tests.

However, my hypothesis is that differences from the mean rate of inflation affect insolvencies (so high or low values of inflation both cause higher insolvencies).For this I think I should use difference of logs of CPI, giving me the inflation rate (and then do the subtraction of the mean). Calculation in stata : abs(d.logCPI - mean(d.logCPI)).

And, I am using the log of Insolvencies as I would expect there to be some exponential growth over time as the number of firms grows.

I have a few questions on this:

1. Should I be testing for stationarity on the raw data or the variations on which my hypothesis is based (d.log CPI and logInsolvencies)

2. Difference of the log of CPI is stationary when I run dfuller, is this therefore I(0) or is it I(1) because the raw data is? My hypothesis is based on the difference of the log so is the percentage change CPI (inflation) technically my raw data?

3. The test on the Insolvencies raw data showed I(1) but the log tests as stationary without differencing so is that therefore I(0)?

Using difference of logs of CPI and the log of Insolvencies will show me the impact (in number of insolvencies) inflation has on it.

Basically, I’m trying to understand whether: 1. I should check for stationarity on the raw data, the changed data, or both. 2. How this is interpreted with order of integration. 3. If the log of the data appears to be stationary, does that imply it is integrated to I(1)?

• This question is squarely on-topic here because its central content is statistics. However, if you are dissatisfied with the economic component of the answers, you may find the Economics site to be better-suited to your needs. – Sycorax says Reinstate Monica Sep 30 '16 at 14:46