Is it possible to tell anything about market structure if I have annual price data of the industries? I have three goods:


beer
carp (fish)
museum ticket


Is it possible to tell anything about market structure if I have annual price data of the industries? Here's the time-series plot on a single graph:

I would like to give advice whether a firm should entry the market or not. Is is it possible to decode price data like "the incumbent firms must have been playing a Bertrand's price competition game at the carp market"? Or do I need further details to say anything about the market structure?

Is it possible to apply IO theory if I have only price data of an industry? I really need some clues, please.
That that we have linear supply and demand functions, pretty much the simplest case such that quantity supplied of good $i$ is:
$$ Q_{s,i,t} = \alpha_{0,i,t} + \alpha_{1,i,t} \cdot P_{i,t}$$
and quantity demanded is:
$$ Q_{d,i,t} = \beta_{0,i,t} + \beta_{1,i,t} \cdot P_{i,t}$$

In equilibrium  $Q_{i,t}=Q_{d,i,t}=Q_{s,i,t}$ so substitute and solve:
$$ Q_{i,t} = \alpha_{0,i,t} + \alpha_{1,i,t} \cdot P_{i,t} = \beta_{0,i,t} + \beta_{1,i,t} \cdot P_{i,t}$$
$$ P_{i,t} = \frac{\alpha_{0,i,t}-\beta_{0,i,t}}{\beta_{1,i,t} - \alpha_{1,i,t}}$$

As you can see, the price depends on supply and demand. Unfortunately, shifts to the level or slope of either the supply or demand functions both affect the price. Therefore, in  general, you can't tell anything about the supply function from the behavior of the price. And if you can't tell anything about the supply function I don't see how you'd know anything about the IO of the producer industries.