Time homogeneous windows applied to finance

Abstract

In finance, quantities varying over time are key for a proper understanding of markets, world trends or simply the evolution of a company. In many cases, detecting a time horizon over which certain quantities can be approximated by a constant is therefore important. As a technique to detect these so-called homogeneity windows has been developed, we will try to examine, insofar as possible, on two new application fields, if these can turn out to be useful for practitioners. The first part of this thesis proposes a solution to the question of the time horizon selection over which to compute the market risk factor loading as used in the Capital Asset Pricing Model. As the selection of this horizon is often arbitrary in the industry, coming up with a rational method seems to fill a gap. For this purpose, we develop statistical tests and algorithms to estimate the risk factor loading and propose a new test to check the estimation quality in practise. It turns out that our method performs at least at good as the classical method used by practitioners on a financial application and displays better adaptability capabilities, in particular when regimes change. This is however counterbalanced by a slightly poorer R squared. The second model aims at assessing the predictive capability of such homogeneity windows for both the mean and the variance of an asset process using a logistic regression. In this model the estimated values as well as the length of the time interval are considered as explanatory variables. The results are twofold. On the one hand, it seems that there is useful information contained in our aggregated data. Besides, the model is able to detect known empirical facts observed on financial markets. On the other hand, this particular, rather basic setting is not able to clearly distinguish ups from downs and can therefore not yield an economical benefit, which is in line with empirical observations concerning market efficiency.