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I want to predict relative outperformance between a stock and an associated benchmark index using time-series models (e.g. ARIMA, LSTM) and some exogenous variables (day of the week, corporate actions etc.) on a weekly basis.

Two different statisitcal designs come to my mind:

  • Estimate and predict the returns for stock and benchmark index separately and calculate outperformance based on the two predicted returns
  • Calculate outperformance beforehand and use this to estimate the model and predict outperformance directly

What could be statistical implications or pros and cons using the one or other approach (e.g. still having a stationarity process in approach 2 etc.)?

Any feedback appreciated!

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