Searching optimum ranges for maximizing a variable

I am currently working on a project where I have been asked to analyze a dataframe with various time series.

       signal_alpha signal_beta ... signal_omega
idx
time_a   value          value          value
time_b     .               .               .
...        .               .               .
time_n     .               .               .


Let us pretend that signal_omega is the variable that I would like to maximize. Is there a mathematical method to analyze and return the ranges for maximize that variable in function of the others?

• Are you trying to predict omega according to other values, or just omega according to its past values? Or both? Commented Oct 18, 2022 at 12:29
• I am only finding optimal ranges of the other variables for maximize omega. (do not know if i can edit comments, sorry) Commented Oct 19, 2022 at 8:54

1 Answer

There are various ways to deal with this kind of data, but I think you could consider it as a multivariate time series problem.

First because you have a time logic in every column that could be learned by a model to detect patterns in a sequential way.

Then because there could be correlations between values that could improve the results.

That's why I suggest to do some correlation map between features to know better the data.

https://seaborn.pydata.org/examples/many_pairwise_correlations.html

Then, it seems that you want to "optimize" omega, which makes me think more about an optimization algorithm like Reinforcement Learning or Genetic Algorithm.

The simplest one is the Genetic Algorithm. It would explore thousands of random data to find an optimum, and the results are usually very good compared to human ones.

Here are some useful links to implement it:

https://medium.com/analytics-vidhya/creating-genetic-algorithms-with-python-187d79f27c0a

https://bobrupakroy.medium.com/auto-time-series-411453a78562

• @Islen does it answer your question? If not, please let me know. Commented Oct 21, 2022 at 7:38
• I don't know how could i use these techniques for search the optimal ranges of alpha, beta... for maximize omega, could you be precise? thanks. Commented Oct 26, 2022 at 9:41
• This could require some investigation. As the problem seems complex, the solution is probably complex too. Some additional details could be helpful to find the right solution. I recommend studying thoroughly how multi-variate time series work donskerclass.github.io/Forecasting/MultivariateForecasts.html Commented Oct 30, 2022 at 8:01