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I want to predict relative outperformance between a stock and an associated benchmark index using statistical time-series models (e.g. ARIMA) 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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    $\begingroup$ Prediction in Finance is extremely difficult. In the first method you would have to build not 1 but 2 predictive models and have both work well enough that their preds can be compared. The second method seems simpler, with only one observable variable to predict. And the precision of the prediction is not as important, with the correct sign already considered a success. Being lazy I prefer 2d method. $\endgroup$
    – noob2
    Jun 26 at 15:02
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If I have understood your question correctly, the first approach would be better:

This is just my thoughts, which stems from intuition: For two forecasted returns of the financial assets, you will always be able to calculate a predicted outperformance value and compare it to the realized version when available. However, forecasting the outperformance metric only (assuming it is some sort of transformation/distance measure between the forecasted returns) you will not be able to back out the values of both forecasted returns (accurately). Therefore, the first method offers you the freedom to use alternative metrics and statistical evaluations on the forecasted returns, giving you a more nuanced picture of your predictions as-well as your statistical models.


In the end, you can do both. Try and observe how much the forecasted outperformance metric (found from a statistical model, ie. your second method) deviates from the realized counterpart as-well as the forecasted outperformance metric calculated from the forecasted returns (your first method). See which method is closer to the realized values. If the difference is marginal, I would opt for the first method.

Nevertheless, if your only goal is to forecast the outperformance metric, then the second method should be fine. If you want to do an extensive analysis on the financial assets, including alternative metrics and statistical evaluations, then the first method should be your choice. I hope this provides some feedback.

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