The basic idea is that given a financial time series of N periods with three states (up, neutral, or down) there are 3^N possible "strategies" to test, which is

The basic idea is that given a financial time series of N periods with three states (up, neutral, or down) there are 3^N possible "strategies" to test, which is an NP problem. This doesn't seem right. It's completely atheoretical and ignores the market or asset structure. The question is not how many strategies there are, but how hard is it to compute the optimal price. Basic economic theory often can be used to derive the optimal price as a simple function of information (data). There may an argument that markets are inefficient that follows an NP=P style argument, but I suspect it would require a specific market structure, such as a set of agents that can only communicate via a sparse network.