This research develops and applies nonparametric estimation tools in two sectors of interest of financial econometrics: risk management and market microstructure. In the first part we address the problem of estimating conditional quantiles in financial and economic time series. Research in this field received great impulse since quantile based risk measures such as Value at Risk (VaR) have become essential tools to assess the riskiness of trading activities. The great amounts of data available in financial time series allows building nonparametric estimators that are not subject to the risk of specification error of parametric models. A wavelet based estimator is developed. With this approach, minimum regularity conditions of the underlying process are required. Moreover the specific choice of the wavelets in this work leads to the constructions of shape preserving estimators of probability functions. In other words, estimates of probability functions, both densities and cumulative distribution functions, are probability functions themselves. This method is compared with competing methods through simulations and applications to real data. In the second part we carry out a nonparametric analysis of financial durations, that is of the waiting times between particular financial events, such as trades, quote updates, volume accumulation, that happen in financial markets. These data display very peculiar stylized facts one has to take into account when attempting to model them. We make use of an existing algorithm to describe nonparametrically the dynamics of the process in terms of its lagged realizations and of a latent variable, its conditional mean. The estimation devices needed to effectively apply the algorithm to our dataset are presented in this part of the work.

Yes / New orthogonal wavelet transforms can be designed by changing the wavelet basis functions or by constructing new low-pass filters (LPF). One family of wavelet may appeal, in use, to a particular application than another. In this study, the wavelet transform based on raisedcosine spectrum is used as an independent orthogonal wavelet to study multicarrier modulation behaviour over multipath channel environment. Then, the raised-cosine wavelet is compared with other well-known orthogonal wavelets that are used, also, to build multicarrier modulation systems. Traditional orthogonal wavelets do not have side-lobes, while the raised-cosine wavelets have lots of side-lobes; these characteristics influence the wavelet behaviour. It will be shown that the raised-cosine wavelet transform, as an orthogonal wavelet, does not support the design of multicarrier application well like the existing well-known orthogonal wavelets.

Yes / The Daubechies, coiflet and symlet wavelets, with properties of orthogonal wavelets are suitable for multicarrier transmission over band-limited channels. It has been shown that similar wavelets can be constructed by Lagrange approximation interpolation. In this work and using established wavelet design algorithms, it is shown that ideal filters can be approximated to construct new orthogonal wavelets. These new wavelets, in terms of BER behave slightly better than the wavelets mentioned above, and much better than biorthogonal wavelets, in multipath channels with additive white Gaussian noise (AWGN). It is shown that the construction, which uses a simple simultaneous solution to obtain the wavelet filters from the ideal filters based on established wavelet design algorithms, is simple and can easily be reproduced.