Whenever we make a prediction we will make an error of a varying degree. What is worse,positive errors or negative ones? This question is important to answer before estimating amodel. When estimating a model a loss function is chosen, a function that gives an instruction of how to transform a particular error. Previous research hints at applications whereasymmetric loss functions provide more optimal models than using symmetric loss functions.Through a simulation study, this thesis highlights the consequences of using symmetric andasymmetric loss functions when assuming the actual problem is asymmetric. This thesis isconducted to cover a gap in literature as well as to correct a common statistical misunderstanding. Our core findings are that the models that take the asymmetry into account havethe lowest prediction errors, while also demonstrating that the larger the degree of asymmetry leads to a greater difference in performance between asymmetric and symmetric modelsin favour of the models estimated with asymmetric loss functions. This confirms what isdemonstrated in existing literature and what can be found in statistical theory.

In this study a structural model of the South African stock market, the Johannesburg Stock Exchange (JSE), was developed and estimated econometrically. The study has made three important contributions to the literature. Firstly, a structural model of the South African stock market has been developed, which quantifies the relationships between the stock market and macroeconomic variables while analyzing the impact of foreign markets and phenomena such as contagion, policy changes and structural economic changes on the JSE. This will improve the economic agents’ understanding of the functioning of the stock market and potentially assist in forecasting the stock market. Secondly, investors are generally assumed to be risk and/or loss averse. This study explains how this risk and/or loss aversion of investors can cause asymmetry in stock prices and the study evaluates different types of stock market asymmetry with advanced econometric techniques such as the threshold cointegration test of Siklos and Enders (2001) and a Markov switching regime model. The Markov switching regime model is used to model the South African business cycle and to construct an indicator for the state of the business cycle, which is in turn used to introduce cyclical asymmetry in the stock market model. The Markov switching regime model is in itself a substantial contribution to the literature since no Markov switching regime model has been estimated for the South African business cycle yet. Apart from being used to capture cyclical asymmetry in the stock market, the Markov switching regime business cycle model can also be used to identify turning points in the South African economy and to model economic growth. Finally, the forecasting performance of the stock market model developed in this study is compared to other stock market models. According to the results, this model is preferred to the other stock market models in terms of modelling and forecasting the level and direction of the JSE. This means that investors and policy markets can use this model to simulate the impact of changes in macroeconomic indicators on the future course of the stock market and use it to develop profitable trading rules. / Thesis (PhD (Econometrics))--University of Pretoria, 2005. / Economics / unrestricted

Uma questão interessante na política monetária é se os Bancos Centrais dão pesos iguais para desvios positivos e negativos da inflação e do hiato do produto das suas respectivas metas. Para responder à esta questão, estimou-se a função perda da autoridade monetária não parametricamente através do método de sieve estimator, expandindo-a através de uma base composta de polinômios ortogonais. A economia foi modelada com agentes foward-looking e com comprometimento por parte da autoridade monetária. O método foi aplicado para a os Estados Unidos desde 1960 e para o Brasil a partir de 1999. Para a economia norte-americana não foram encontradas evidências de assimetria nas preferências da autoridade monetária. Já no Brasil o Banco Central mostrou ter preferências assimétricas quanto à inflação, auferindo uma maior perda de desvios negativos do que positivos em relação à meta. / An interesting question in monetary policy is whether the Central Bank gives equal weights to positive and negative deviations of inflation and output gap from their targets. Trying answering this question, we estimated the monetary authority’s loss function nonparametrically, using the method of sieves, expanding it with orthogonal polynomials. The economy was model with forward-looking agents and with commitment of the monetary authority. We applied the method to U.S. monetary policy since 1960 and for Brazil since 1999. For the U.S. economy, it was not found evidence of asymmetry in the preferences of the monetary authority. In Brazil, the Central Bank proved to have asymmetric preferences about inflation, with a greater loss for negative deviations of inflation from the target rather for positive ones.

Uma questão interessante na política monetária é se os Bancos Centrais dão pesos iguais para desvios positivos e negativos da inflação e do hiato do produto das suas respectivas metas. Para responder à esta questão, estimou-se a função perda da autoridade monetária não parametricamente através do método de sieve estimator, expandindo-a através de uma base composta de polinômios ortogonais. A economia foi modelada com agentes foward-looking e com comprometimento por parte da autoridade monetária. O método foi aplicado para a os Estados Unidos desde 1960 e para o Brasil a partir de 1999. Para a economia norte-americana não foram encontradas evidências de assimetria nas preferências da autoridade monetária. Já no Brasil o Banco Central mostrou ter preferências assimétricas quanto à inflação, auferindo uma maior perda de desvios negativos do que positivos em relação à meta. / An interesting question in monetary policy is whether the Central Bank gives equal weights to positive and negative deviations of inflation and output gap from their targets. Trying answering this question, we estimated the monetary authority’s loss function nonparametrically, using the method of sieves, expanding it with orthogonal polynomials. The economy was model with forward-looking agents and with commitment of the monetary authority. We applied the method to U.S. monetary policy since 1960 and for Brazil since 1999. For the U.S. economy, it was not found evidence of asymmetry in the preferences of the monetary authority. In Brazil, the Central Bank proved to have asymmetric preferences about inflation, with a greater loss for negative deviations of inflation from the target rather for positive ones.

Uma questão interessante na política monetária é se os Bancos Centrais dão pesos iguais para desvios positivos e negativos da inflação e do hiato do produto das suas respectivas metas. Para responder à esta questão, estimou-se a função perda da autoridade monetária não parametricamente através do método de sieve estimator, expandindo-a através de uma base composta de polinômios ortogonais. A economia foi modelada com agentes foward-looking e com comprometimento por parte da autoridade monetária. O método foi aplicado para a os Estados Unidos desde 1960 e para o Brasil a partir de 1999. Para a economia norte-americana não foram encontradas evidências de assimetria nas preferências da autoridade monetária. Já no Brasil o Banco Central mostrou ter preferências assimétricas quanto à inflação, auferindo uma maior perda de desvios negativos do que positivos em relação à meta. / An interesting question in monetary policy is whether the Central Bank gives equal weights to positive and negative deviations of inflation and output gap from their targets. Trying answering this question, we estimated the monetary authority’s loss function nonparametrically, using the method of sieves, expanding it with orthogonal polynomials. The economy was model with forward-looking agents and with commitment of the monetary authority. We applied the method to U.S. monetary policy since 1960 and for Brazil since 1999. For the U.S. economy, it was not found evidence of asymmetry in the preferences of the monetary authority. In Brazil, the Central Bank proved to have asymmetric preferences about inflation, with a greater loss for negative deviations of inflation from the target rather for positive ones.

No description available.

Die generalisierte Quantilregression, einschließlich der Sonderfälle bedingter Quantile und Expektile, ist insbesondere dann eine nützliche Alternative zum bedingten Mittel bei der Charakterisierung einer bedingten Wahrscheinlichkeitsverteilung, wenn das Hauptinteresse in den Tails der Verteilung liegt. Wir bezeichnen mit v_n(x) den Kerndichteschätzer der Expektilkurve und zeigen die stark gleichmßige Konsistenzrate von v-n(x) unter allgemeinen Bedingungen. Unter Zuhilfenahme von Extremwerttheorie und starken Approximationen der empirischen Prozesse betrachten wir die asymptotischen maximalen Abweichungen sup06x61 |v_n(x) − v(x)|. Nach Vorbild der asymptotischen Theorie konstruieren wir simultane Konfidenzb änder um die geschätzte Expektilfunktion. Wir entwickeln einen funktionalen Datenanalyseansatz um eine Familie von generalisierten Quantilregressionen gemeinsam zu schätzen. Dabei gehen wir in unserem Ansatz davon aus, dass die generalisierten Quantile einige gemeinsame Merkmale teilen, welche durch eine geringe Anzahl von Hauptkomponenten zusammengefasst werden können. Die Hauptkomponenten sind als Splinefunktionen modelliert und werden durch Minimierung eines penalisierten asymmetrischen Verlustmaßes gesch¨atzt. Zur Berechnung wird ein iterativ gewichteter Kleinste-Quadrate-Algorithmus entwickelt. Während die separate Schätzung von individuell generalisierten Quantilregressionen normalerweise unter großer Variablit¨at durch fehlende Daten leidet, verbessert unser Ansatz der gemeinsamen Schätzung die Effizienz signifikant. Dies haben wir in einer Simulationsstudie demonstriert. Unsere vorgeschlagene Methode haben wir auf einen Datensatz von 150 Wetterstationen in China angewendet, um die generalisierten Quantilkurven der Volatilität der Temperatur von diesen Stationen zu erhalten / Generalized quantile regressions, including the conditional quantiles and expectiles as special cases, are useful alternatives to the conditional means for characterizing a conditional distribution, especially when the interest lies in the tails. We denote $v_n(x)$ as the kernel smoothing estimator of the expectile curves. We prove the strong uniform consistency rate of $v_{n}(x)$ under general conditions. Moreover, using strong approximations of the empirical process and extreme value theory, we consider the asymptotic maximal deviation $\sup_{ 0 \leqslant x \leqslant 1 }|v_n(x)-v(x)|$. According to the asymptotic theory, we construct simultaneous confidence bands around the estimated expectile function. We develop a functional data analysis approach to jointly estimate a family of generalized quantile regressions. Our approach assumes that the generalized quantiles share some common features that can be summarized by a small number of principal components functions. The principal components are modeled as spline functions and are estimated by minimizing a penalized asymmetric loss measure. An iteratively reweighted least squares algorithm is developed for computation. While separate estimation of individual generalized quantile regressions usually suffers from large variability due to lack of sufficient data, by borrowing strength across data sets, our joint estimation approach significantly improves the estimation efficiency, which is demonstrated in a simulation study. The proposed method is applied to data from 150 weather stations in China to obtain the generalized quantile curves of the volatility of the temperature at these stations