if a precipitation or temp time series comes out to be inhomogeneous after applying diff statistical tests....then it should be discarded and not used in future anlysis?
Due to several factors, such as instrument calibration and relocation, raw climate measurements may contain non-climatic jumps or biases. Thus, you may use the relative homogenization approach to compare a candidate station with reference time series based on multiple neighboring stations.
You may identify and remove the non-climatic changes that happen in the station. If you find a systematic noise (e.g., shift or jump in trend) in the time series corresponding to the station, then you may apply an appropriate model and remove the noise from the time series.
You can use ANN for your data (with inhomogeneous). Since ANN (based on RNN, GRU, LSTM, MLP) models perfectly cope with such types of data.
In principle, I can try to develop a ANN model for you. I'm working on python using KERAS and TensorFlow. My contacts: [email protected] or WhatsApp(+79322301628).