Repositori URV

Identifier: TDX:1308

Handle: https://hdl.handle.net/20.500.11797/TDX1308

Authors:
Cano Berlanga, Sebastian

Abstract:
When a database contains missing values, the forthcoming analysis becomes impossible until one decides how to deal with them. That is the reason why the literature has developed different ways to solve problems associated with NA values. The first methods of this specific literature were regression-based (Yates [1933]), but later more sophisticated algorithms were available (EM algorithm). Rubin [1987] makes a deep analysis on the topic and develops Multiple Imputation, a Monte Carlo technique in which the missing values are replaced by m>1 simulated versions, where m is typically small (e.g. 3-10). In Rubin's method for `repeated imputation' inference, each of the simulated complete datasets is analyzed by standard methods, and the results are combined to produce estimates and confidence intervals that incorporate missing-data uncertainty. Multiple Imputation has been widely used in cross section studies but not in time series. This doctoral thesis aims to extend Multiple Imputation to longitudinal studies, specifically to financial time series. To do so, we propose a method based on an asymmetric filter which splits the original time series in conditional variance and innovations. This procedure allows us to generate plausible values combining the algorithms Gibbs Sampling and Approximate Bayesian Bootstrap. The validity of the proposed method is discussed through extensive tests on different financial time series (firms and market indices). The analysis of empirical tests displays that, after imputing the data, they maintain its individual characteristics. Furthermore, results exhibit high precision in the shape parameter of the conditional distribution of returns, and densities of both conditional variance and innovations.