can the tsoutliers package be applied on non-stationary time series and standardized level residuals? can the tsoutliers package be applied to standardized level residuals to obtain better locations of changepoints or is the package applicable only on the original time series data?
for example i tried applying the package to the original data and obtained:
Outliers:

and when I applied the package to the standardized level residuals I got this:
Outliers:

also, is the package applicable to Non-stationary time series?
 A: You can use the package on any time series as such but it is advised to use it on original time series. Reason is simple. The package is based on the seminal paper by Chen & Liu (1993). The title of this paper is Joint Estimation of Model Parameters and
Outlier Effects in Time Series.
The key word here is 'Joint Estimation'. The idea is that outliers influences model selection in ARIMA modeling. So if you use residuals, you have fixed the model and then looking for outliers - ignoring that you may not have chosen the best model due to presence of outliers and thereby not detecting outliers also efficiently.
Even if your model selection is somehow not influenced by outliers, the estimates of coefficients will be affected by not doing a simultaneous estimation. Therefore, it is best to apply tso on original time series.
On the question of non-stationary data. Yes you can use tso directly on non-stationary data as the package models series as ARIMA (not ARMA). So model selection is based on internal testing for non-stationary as well.
For details see the paper of package vignette.
