Kernel Density Smoothing Using Probability Density Functions and Orthogonal Polynomials
This article is the first of a series devoted to providing a way to
correctly explore stock market data through kernel smoothing
methods. Here, we are mainly interested in kernel density smoothing,
our approach revolves around introducing and testing the goodness of
fit of some non-classical kernels based on probability density functions
and orthogonal polynomials, the latter ones are of interest to us when
they are of order two and above. For each kernel, we use a
modified version of the “rules of thumb” principle in order to
compute a smoothing parameter that would offer optimal smoothing
for a reasonable computational cost. Compared to the Gaussian
kernel, some of the tested kernels have provided a better
Chi-square statistic, especially the kernels of order 2 based on
Hermite and Laguerre polynomials. These results are illustrated
using data from the Moroccan stock market.
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