How did the tax rate change in the last 10 epochs?

Let's answer the bounty question first, then we can explore what made the changes occur.

Tax decreases in May and continues to fall until mid June. From there we can see an upwards trend. Now, lets understand how the tax rate is determined so that we can answer what might have influenced this behavior.

How is the tax rate determined?

Tax Rewards (T): Income generated from transaction fees (stability fee) in a during the epoch.

Total Staked Luna (SL): Total Luna that has been staked by users and bonded by their delegated validators.

Tax Reward Per Unit Luna: T/SL

Consider R to be the current Tax Rate, and I to be the MiningIncrement parameter.

1- Calculate the rolling average Y of Tax Rewards per unit Luna over the last year.

2- Calculate the rolling average M of Tax Rewards per unit Luna over the last month.

3- If M = 0, there was no tax revenue in the last month. The Tax Rate should thus be set to the maximum permitted by the Tax Policy.

4-Otherwise, the new Tax Rate is , (I * R * Y) / M

Of course both 3 and 4 are subject to the rules of pc.Clamp()

What might have caused the changes?

Since the tax rate is depends on Tax rewards(Transaction Fees) and Total Staked Luna we can check the charts below to understand why the tax falls between mid May - mid June and rises afterwards.

Conclusion

Between mid May - mid June the tax rate decreases because there is a steep increase in short term tax rewards (transaction fees) that is not mirrored in total staked luna amount. Since the tax revenues in a shorter time window performs in such a good way and this sharp rise is not seen in total staked luna amount the tax rate falls to compensate. After this unusual tax reward increase in the last two weeks of May leaves the short term window (1 month) and there is a sharp increase in total staked luna, Tax rate starts to increase once more.