I am currently investigating the inflation persistence for different countries by using R.

I took data from the OECD for Sweden (1993-2017) and checked first if the series is stationary with the ur.df-test (type = "none"). The Value of test-statistic is: -1.1454 and with critical values of -1,95 (for the 5pct-level) the $H_0$ (unit root) cannot be rejected.

Results ADF:

           Estimate Std. Error t value Pr(>|t|)
z.lag.1     -0.1944     0.1697  -1.145    0.265
z.diff.lag  -0.2317     0.2296  -1.009    0.324

However, I tried fitting an AR(1) model (order choosen by AIC) to the data which gives the following output:

> coeftest(model4)

z test of coefficients:

          Estimate Std. Error z value  Pr(>|z|)    
ar1        0.34592    0.18522  1.8675   0.06183 .  
intercept  1.72133    0.42947  4.0081 6.122e-05 ***

Now my question:

Why is the estimate for ar(1) so far below 1?

It was my understanding that you can get a hint from this estimate if the model is stationary. So if its absolute value is around 1 then you get a hint for non-stationarity. Or is this wrong? By seeing this estimate i would not have guessed that it is not stationary.

Maybe you can shed some light on this for me. And if you have additional comments to this method, please let me know.


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