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I have created a trading strategy which operate every single day on the DAX 30, for the last 1700 trading sessions (some years). I have the daily returns of my strategy and also the daily returns of my index. I'm using R, therefore i can get sd, mean, var ecc...

The big issue that impresses the market watchers and financial types is the ability to consistently make above-market returns.

What are the main important instrument to test the significance of a trading strategy?Is it sufficient a simple t-test? Which type (paired, unpaires ecc..)? What are your suggestions?

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    $\begingroup$ Read this "Pseudo-Mathematics and Financial Charlatanism: The Effects of Backtest Overfitting on Out-of-Sample Performance" in "Notices of the AMS", freely available at ams.org/notices/201405/rnoti-p458.pdf . It's easy to beat the market - anyone can do it in backtesting..In real life, it's not as easy. $\endgroup$ – Mark L. Stone Aug 18 '16 at 22:19
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    $\begingroup$ Although on-topic on Cross Validated, this question may well get better informed answers at quant.stackexchange.com (the Quantitative Finance SE) - you can ask a moderator to migrate it for you using the "flag" button at the bottom of the post. Answers on CV will tend to be statistically oriented, answers on Quant SE may be better for the financial/trading implications. $\endgroup$ – Silverfish Aug 18 '16 at 22:26
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The most obvious choice should be an one-sided paired t-test, since what you want to tell is if the difference of your strategy return and the market return for the same days is significantly greater than zero. However, two caveats should be taken in account:

  • Multiple comparisons: If you have created more than one trading strategy, significance of the best one will be misleading.
  • Non independence of daily returns. T-test (and other test) assume independence of all values in a sample. Returns on a day may be correlated with returns in previous days.
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    $\begingroup$ See my comment above. $\endgroup$ – Mark L. Stone Aug 18 '16 at 22:22

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