Advances in boosting of temporal and spatial models

Robinzonov, Nikolay (2013): Advances in boosting of temporal and spatial models. Dissertation, LMU München: Fakultät für Mathematik, Informatik und Statistik

Abstract

Boosting is an iterative algorithm for functional approximation and numerical optimization which can be applied to solve statistical regression-type problems. By design, boosting can mimic the solutions of many conventional statistical models, such as the linear model, the generalized linear model, and the generalized additive model, but its strength is to enhance these models or even go beyond. It enjoys increasing attention since a) it is a generic algorithm, easily extensible to exciting new problems, and b) it can cope with``difficult'' data where conventional statistical models fail. In this dissertation, we design autoregressive time series models based on boosting which capture nonlinearity in the mean and in the variance, and propose new models for multi-step forecasting of both. We use a special version of boosting, called componentwise gradient boosting, which is innovative in the estimation of the conditional variance of asset returns by sorting out irrelevant (lagged) predictors. We propose a model which enables us not only to identify the factors which drive market volatility, but also to assess the specific nature of their impact. Therefore, we gain a deeper insight into the nature of the volatility processes. We analyze four broad asset classes, namely, stocks, commodities, bonds, and foreign exchange, and use a wide range of potential macro and financial drivers. The proposed model for volatility forecasting performs very favorably for stocks and commodities relative to the common GARCH(1,1) benchmark model. The advantages are particularly convincing for longer forecasting horizons. To our knowledge, the application of boosting to multi-step forecasting of either the mean or the variance has not been done before. In a separate study, we focus on the conditional mean of German industrial production. With boosting, we improve the forecasting accuracy when compared to several competing models including the benchmark in this field, the linear autoregressive model. In an exhaustive simulation study we show that boosting of high-order nonlinear autoregressive time series can be very competitive in terms of goodness-of-fit when compared to alternative nonparametric models. Finally, we apply boosting in a spatio-temporal context to data coming from outside the econometric field. We estimate the browsing pressure on young beech trees caused by the game species within the borders of the Bavarian Forest National Park ``Bayerischer Wald,'' Germany. We found that using the geographic coordinates of the browsing cases contributes considerably to the fit. Furthermore, this bivariate geographic predictor is better suited for prediction if it allows for abrupt changes in the browsing pressure.

• Dokumententyp: Dissertationen (Dissertation, LMU München)
• Themengebiete: 500 Naturwissenschaften und Mathematik ; 500 Naturwissenschaften und Mathematik > 510 Mathematik
• Fakultäten: Fakultät für Mathematik, Informatik und Statistik
• Sprache der Hochschulschrift: Englisch
• Datum der mündlichen Prüfung: 30. Januar 2013
• 1. Bericht­erstatter:in: Hothorn, Torsten