In the modeling of financial time series, mathematicians have always incurred limits when trying to fit models to datasets. It seems like the evolution of market phenomena is too complex to be captured by an easy parametric model. In 2003, Politis introduced a modelfree data-based approach that he named NoVaS (Normalizing and Variance Stabilizing) method. As no particular model is invoked, the loss of information whilst fitting a model to the data is avoided. At the same time, due to its parsimony, NoVaS is a very intuitive and numerically feasible approach.In this thesis, we give an overview of the existing NoVaS theory in an univariate setting and extend it to the case of multivariate time series.We then introduce possible applications of the methodology, including the construction of minimum variance portfolio and intuitive estimation of parameters of a GARCH(1; 1) process without invoking likelihood methods. In the meantime, we lead an empirical analysis, in which we compare the performance of NoVaS to standard methods in the literature in a multivariate setting.     «

In the modeling of financial time series, mathematicians have always incurred limits when trying to fit models to datasets. It seems like the evolution of market phenomena is too complex to be captured by an easy parametric model. In 2003, Politis introduced a modelfree data-based approach that he named NoVaS (Normalizing and Variance Stabilizing) method. As no particular model is invoked, the loss of information whilst fitting a model to the data is avoided. At the same time, due to i...     »