May anybody correct this, please?

In this paper, the existence of cyclical behavior patterns in the balance between supply and demand of the global MAM market is researched.

Excellent! I think you can simplify this sentence by taking out "the existence of" and just having "In this paper, cyclical beahvior patterns in the balance between supply and demand of the global MAM market are researched." I would also replace 'researched' with 'examined' or 'analyzed'.

For this purpose, tension indicators on the market, from detailed historical data, are selected and calculated and analyzed their temporal evolution.
I'm not exactly sure what 'tension indicators' are, but I think the sentence would sound more idiomatic as, "For this purpose (or 'Towards this end'), indicators of tension on the market are gathered and calculated from detailed historical data, and their change over time is analyzed.
The primary method of analysis to be used is the harmonic analysis, in which, it is intended to deduce the existence of these cyclical patterns in the evolution of indicators.

Again, you can take out some wording near the beginning of the sentence to make it simpler. "Harmonic analysis will be used to deduce the existence of these cyclical patterns in the evolution of the indicators."

After deducting deducing the existence of this behavior, the dynamics governing cycles will be investigated more thoroughly. Thus, it will deepen investment cycles in the MAM industry and its relationship to supply and demand cycles.

I can't really be much help in this last sentence. I'm not familiar with what you're writing about, so I don't want to change something and make it scientifically incorrect.

* This paper has to be very formal, so if you think there are better connector to use, please, tell me.

Overall, this is excellent! There are very few actual grammar mistakes; the main thing to work on is making your ideas flow more smoothly by making some sentences a little less wordy.