Numerical Probability Density Function from Characteristic Function

Computes a numerical probability density function starting from a Characterstic function.

This function computes the numerical probability density function of the convolution of the Fourier Transforms of a standard mean reverting process without long term mean level and a mean reverting process presenting a jump rather than a diffusion. From such a numerical probability density function it is possible to estimate the parameter values running a standard maximum likelihood procedure. This machinery represents a good choice when modelling variables that present peaks in their distribution that fastly come back to their mean level.
The function takes as inputs the sample space, the initial values for the processes X and Y and the values of the parameters for the two considered processes. When one desires to estimate such parameters via maximum likelihood, just run the Matlab function mle, taking as input conv_pdf and the considered sample data.
Example:
x = -1:0.01:3;
init = [0 0];
param = [5 0.2 20 0.5 0.1 0.2]