I created a strategy using a regression on a price series. I tested it with many walk-forward analyses and it has passed. I am currently live trading it with real capital (the ultimate test). My question is how many live trades have to occur to have a high confidence that I have not overfitted or am subject to short term variance but actually have a statistical edge?
I think your question is somehow missleading.
When one is looking for a good trading strategy that shall be based on statistica/mathematical/econometrical methods he typically proceeds as follows:
Estimates the process that drives the prices, e.g. of stocks. This could be done with a lot of models. For example RW (random walk), CAPM (capital asset pricing model), ARMA-GARCH (Autoregressive moving average with generelized autoregressive conditional heteroscedasticity), ...
Then he performes "tests" of several trading strategies for the estimated proccess to find the best trading strategy for his pourpuse.
Your question "Exactly how many trades are necessary for statistical significance?" doesn't refer to one of the above steps clearly. Statistical significance has to be obtained in step one. Because this is the step where you are estimating something. But the number of you trades are at best showing up in step two (if you simulate the trades numerically). Or they will show up in the end, when you strategy is implemented. Additionally, the question for an 'exact number' seams to be missleading. Typically, answers would be of the 'the more, the etter' type.