Its use is primarily in establishing price lower and upper limits as the function of past proportions occurring in currency/commodity price fluctuations. This effort is similar in how Fibonacci Ratios are used
in the financial trading.
Possible applications in the lottery forecast models could potentially exist providing that parallel analytical proportions do exists. This is very speculative and I could not find any references regarding
stochastic studies using Padovan Sequence. (except financial risk models mentioned before)
I speculate its potential success in commodity financial forecast stem from global proportions arising in the supply/demand cycles, such as natural climate paterns , human/animal migration patterns etc.
However if the Padovan ratios demonstrate success in the currency model, this would rather pose an enigma, as the currency pricing can not be related (as far as i know) to any natural (world) proportions and cycles (supply and demand exists purely as abstraction of an underlying commodity/labour markets), in other words currency trading is very much like an un-bias stochastic game model (aka lottery), and it might be a hidden doorway to deeper view to the random...
1. On Plastic Numbers in the Plane:
1. Properties of Plastic Number: