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Quantitative Finance

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    $\begingroup$ I'm not sure what you're professor means because, at time $(t+1)$, $x_{t}$ is not future information. $\endgroup$ Commented Jun 26 at 14:43
  • $\begingroup$ @markleeds He means that I want to predict $r_{t+1} = \log(x_{t+1}/x_t)$, while my training dataset's $r_t = \log(x_t/x_{t-1})$ contains information of $x_t$, which can leak information. $\endgroup$ Commented Jun 30 at 8:12
  • $\begingroup$ Hi user398843: $log(\frac{x_{T+1}}{x_{T}}) = log(x_{T+1}) - log(x_{T})$, so if time $T$ is the border line where training stops, then returns in the future onwards from T, ALWAYS depend on what the price was in the past but that's not leaking information. It's just computing how much the price increased since time $T$. The information in the training set is being used to compute the performance in the non-trained dataset. If you don't use that, then you won't know what the performance was. $\endgroup$ Commented Jun 30 at 10:35
  • $\begingroup$ user398843: I didn't find my comment above very insightful so here's a better way to think about it. This comment assumes that, by information leakage, your professor means that you are taking information in the training set and using it as valid information in the non-training data set. This is not what is being done here. All you are doing here is using the information in the training set to calculate the return performance in the non-trained data set. But, as far as I can see, $x_t$ is not being used in any other way. It's like an anchor for performance one step ahead. $\endgroup$ Commented Jun 30 at 20:25
  • $\begingroup$ @markleeds Thank you for your comments. I greatly appreciate it! Do you know why there is a large difference in the accuracy of our prediction when using "the average mid-price of each bin" versus "the last tick's mid-price of each bin" as $x_t$? $\endgroup$ Commented Jul 2 at 7:49