I want to generate synthetic forex data for the purpose of backtesting my trading algorithms. I have some rough ideas in mind on how to do this:
Start with a curve representing a trend, then randomly generate points around the curve according to a Gaussian or some other distribution. Then take the generated points and somehow generate the bar data (open, high, low, close) around those points; alternatively, add a time factor, and then randomly determine when a tick occurs and collect the data into bars afterward.
My question is: is this far off from the established methods for synthetic data generation? I suppose that raises the more basic question: are there any established methods for synthetic data generation? I can't seem to find any writing on this subject, be it a blog post or a research paper.
So in addition to a request for external resources on synthetic data generation, I'd like to know what sorts of distributions best model the relationships between open, high, low, close, or how to generate the appropriate intervals between ticks, the spread between ask and bid prices, etc.