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What is best procedure to normalize the time series data. May I use a unit root test or simply proceed with $\frac{x-min}{max-min}$?

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You seem to be confusing two separate concepts:

  • Unit root tests are used to determine whether a specific type of time series model, namely auto-regressive models, are stationary or not. It is only a test, it doesn't transform the data in any way. Based on the results of the test, you might or you might not want to difference your time series. For more, see ARIMA models.

  • Normalization is used for many things, usually for pre-processing data before feeding it to a machine learning algorithm. If you are using an ML algorithm for time series analysis, you might want to normalize it, but it will depend on which algorithm you are using and what your data looks like.

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