Alternative micropulses and fractional Brownian motion

We showed in an earlier paper (1995a) that negatively correlated fractional Brownian motion (FBM) can be generated as a fractal sum of one kind of micropulses (FSM). That is, FBM of exponent is the limit (in the sense of finite-dimensional distributions) of a certain sequence of processes obtained as sums of rectangular pulses. We now show that more general pulses yield a wide range of FBMs: either negatively (as before) or positively () correlated. We begin with triangular (conical and semi-conical) pulses. To transform them into micropulses, the base angle is made to decrease to zero, while the number of pulses, determined by a Poisson random measure, is made to increase to infinity. Then we extend our results to more general pulse shapes.Fractal sums of pulses Fractal sums of micropulses Fractional Brownian motion Poisson random measure Self-similarity Self-affinity Stationarity of increments

A class of micropulses and antipersistent fractional Brownian motion

We begin with stochastic processes obtained as sums of "up-and-down" pulses with random moments of birth [tau] and random lifetime w determined by a Poisson random measure. When the pulse amplitude [var epsilon] --> 0, while the pulse density [delta] increases to infinity, one obtains a process of "fractal sum of micropulses." A CLT style argument shows convergence in the sense of finite dimensional distributions to a Gaussian process with negatively correlated increments. In the most interesting case the limit is fractional Brownian motion (FBM), a self-affine process with the scaling constant . The construction is extended to the multidimensional FBM field as well as to micropulses of more complicated shape.Fractal sums of pulses Fractal sums of micropulses Fractional Brownian motion Poisson random measure Self-similarity Self-affinity Stationarity of increments

A Class of Pulse Processes

A Class of Pulse Processe

Non-parametric tests of real exchange rates in the post-Bretton Woods era

Long-run PPP, Non-parametric tests, Rescaled R/S test, Rescaled V/S test, F31, C22,