I'm looking for a way to measure the trend of two curves. For example, the figure below is my forecast for the S&P 500. It can be seen that although I haven't predicted the exact index price, the trends of the two curves are quite the same, including the rising and falling time and the turning point time. I have tried distances like DTW and Frechet, but the results are not very good. So is there a way to measure this? enter image description here

Thank for your help!!

  • $\begingroup$ Generally it’s easier to predict returns than prices. In any case, why are the results of DTW and Fréchet not good? $\endgroup$
    – Bob Jansen
    Jun 11, 2022 at 11:55
  • $\begingroup$ Uh.., the result of DTW and Frechet feedback will be a curve entangled with the true value. I think it seems that although the two curves have similar trends, the distance between them is too large. $\endgroup$
    – MoTianao
    Jun 11, 2022 at 12:44
  • $\begingroup$ In addition, I hope that the predicted inflection point will be very close to the true value, but DTW will not consider this point. $\endgroup$
    – MoTianao
    Jun 11, 2022 at 12:59
  • $\begingroup$ @BobJansen, there is a one-to-one relationship between returns and prices, so one cannot be easier to predict than the other. $\endgroup$ Jun 13, 2022 at 7:54
  • $\begingroup$ s/predict/easier to work with $\endgroup$
    – Bob Jansen
    Jun 13, 2022 at 7:55


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