The high frequency data on exchange rates have been given to us by Olsen & Associates, a well known and reputable financial company.
Very often interest rates are modeled as Ornstein-Uhlenbeck process, a stationary Gaussian process. Some say it is good, some say it is not so good.
One would like to investigate -- if the exchange rate is not an Ornstein-Uhlenbeck process, one would want to know why. No Gaussianity?, no stationarity?
Will the huge amount of data -- several changes per second, for 10 years -- reveal anything except noise? If yes, what?
Here is the list of few initial questions:
(a) If on the time-line we join successive prices by short pieces of straight line, we will get a continuous trajectory, which will be practically a fractal set. What is its Hausdorff - Besicovitch
dimension? I think Richard Olsen and Benoit Mandelbrot researched this several years ago, but I suggest the student studies it again, with his/her own
hands. In this way it will be clear what the Hausdorff - Besicovitch dimension is. I believe one very interesting phenomena will be observed on the way.
(b) Is the process Gaussian? And how do we verify this?
(c) Is the process, at least in time horizon of a year, second-order stationary?
(d) If one have had applied a particular strategy, say, if one would have used Renko and Kagi moments (Japanese terms for security trading), would there have
been any advantages?