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Dissertation Defense
March 10 (Mon) 1-2 p.m.
Alavi Commons Room, 6625 Everett Tower
Jaime Burgos
Department of Statistics
Western Michigan University
The increasing needs of forecasting techniques has led to the popularity of the vector autoregressive model in multivariate time series analysis, which has become of typical use across different fields due to its simplicity in application. The traditional method for estimating the model parameters is the least squares minimization, due to the linear nature of the model and its similarity with multivariate linear regression. However, since least squares estimates are sensitive to outliers, more robust techniques have become of interest.
This manuscript investigates a robust alternative by obtaining the estimates using a weighted Wilcoxon dispersion with Schweppe-type weights. The first section introduces the typical definition of a vector autoregressive model, along with popular estimation methods and weighting schemes. In section two, the proposed estimator is shown to be asymptotically multivariate normal, centered about the true model parameters, at a rate of n-1/2. Section three follows with an in depth discussion of the derivation of the main theoretical results. After that, in section four, a Monte Carlo study is presented to evaluate the performance of alternative estimators compared against the least squares estimates. The study results suggest that the Schweppe-weighted Wilcoxon estimates will generally have best performance. This result holds most noticeably under the presence of additive outliers or when the series is closer to non-stationarity. In the last section, the estimation methods are applied to quadrivariate financial time series and results are compared. The applied example results indicate that estimates that use weights are better at detecting outliers by reducing their influence on the fit. This work provides a high efficiency robust alternative to the estimation problem of the vector autoregressive model parameters in multivariate time series analysis.