We consider a time series model with autoregressive conditional heteroskedasticity that is subject to changes in regime. The regimes evolve according to a multistate latent Markov switching process with unknown transition probabilities, and it is the constant in the variance process of the innovations that is subject to regime shifts. The joint estimation of the latent process and all model parameters is performed within a Bayesian framework using the method of Markov Chain Monte Carlo simulation. We perform model selection with respect to the number of states and the number of autoregressive parameters in the variance process using Bayes factors and model likelihoods. To this aim, the model likelihood is estimated by combining the candidate's formula with importance sampling. The usefulness of the sampler is demonstrated by applying it to the dataset previously used by Hamilton and Susmel who investigated models with switching autoregressive conditional heteroskedasticity using maximum likelihood methods. The paper concludes with some issues related to maximum likelihood methods, to classical model select ion, and to potential straightforward extensions of the model presented here. (author's abstract) / Series: Forschungsberichte / Institut für Statistik

South Africa has become more dependent on portfolio inflow to finance investment and consumption due to the low rate of government and household savings. Therefore, it is important from South Africa‟s perspective to maintain a stable portfolio inflow in order to ensure that the current account deficit does not reach unsustainable levels. However, portfolio inflow is anything but stable in South Africa. The risk associated with this is that when foreigners‟ expectations of South Africa shift, due to any form of instability or risk within the country or even internationally, it leads to massive withdrawals or outflow of funds, which in turn causes the currency to depreciate. The portfolio balance theory on the other hand states that an increase in portfolio inflow leads to the appreciation of the nominal exchange rate, and that this is perceived to work against economic growth. The main objective of this research is to determine the nature of the relationship between exchange rate volatility and portfolio flows, and the extent to which volatility in the exchange rate affect South Africa‟s portfolio inflow. The research uses Vector Autoregressive (VAR) models and quarterly data, ranging from 1995 to 2012 to investigate this relationship. From the VAR models a Granger causality test, as well impulse response functions is used to shed light on the influence of a one-unit shock in both foreign portfolio inflow and exchange rate volatility on the other variables in the model. Exchange rate volatility is measured using both Autoregressive Conditional Heteroscedasticity (ARCH) family models and the conventional standard deviation, in order to control for possible biasness caused by the choice of instrument of volatility. The results showed the nature of the relationship between exchange rate volatility and foreign portfolio inflow to South Africa‟s capital markets can be described as country-dependent and time-varying. South Africa‟s portfolio inflow exhibits high volatility and low persistence that are characteristics normally associated with “hot money”, which is largely driven by foreign investors‟ appetite for short-term speculative gains. The study identified the consistent presence of bidirectional causality between the exchange rate volatility and foreign portfolio inflow to South Africa, irrespective of the measurement of exchange rate volatility. The results also revealed that net portfolio flows are associated with exchange rate appreciation and that foreign portfolio inflow react much stronger to changes in exchange rate volatility than vice versa. / MCom (Risk Management), North-West University, Potchefstroom Campus, 2015

South Africa has become more dependent on portfolio inflow to finance investment and consumption due to the low rate of government and household savings. Therefore, it is important from South Africa‟s perspective to maintain a stable portfolio inflow in order to ensure that the current account deficit does not reach unsustainable levels. However, portfolio inflow is anything but stable in South Africa. The risk associated with this is that when foreigners‟ expectations of South Africa shift, due to any form of instability or risk within the country or even internationally, it leads to massive withdrawals or outflow of funds, which in turn causes the currency to depreciate. The portfolio balance theory on the other hand states that an increase in portfolio inflow leads to the appreciation of the nominal exchange rate, and that this is perceived to work against economic growth. The main objective of this research is to determine the nature of the relationship between exchange rate volatility and portfolio flows, and the extent to which volatility in the exchange rate affect South Africa‟s portfolio inflow. The research uses Vector Autoregressive (VAR) models and quarterly data, ranging from 1995 to 2012 to investigate this relationship. From the VAR models a Granger causality test, as well impulse response functions is used to shed light on the influence of a one-unit shock in both foreign portfolio inflow and exchange rate volatility on the other variables in the model. Exchange rate volatility is measured using both Autoregressive Conditional Heteroscedasticity (ARCH) family models and the conventional standard deviation, in order to control for possible biasness caused by the choice of instrument of volatility. The results showed the nature of the relationship between exchange rate volatility and foreign portfolio inflow to South Africa‟s capital markets can be described as country-dependent and time-varying. South Africa‟s portfolio inflow exhibits high volatility and low persistence that are characteristics normally associated with “hot money”, which is largely driven by foreign investors‟ appetite for short-term speculative gains. The study identified the consistent presence of bidirectional causality between the exchange rate volatility and foreign portfolio inflow to South Africa, irrespective of the measurement of exchange rate volatility. The results also revealed that net portfolio flows are associated with exchange rate appreciation and that foreign portfolio inflow react much stronger to changes in exchange rate volatility than vice versa. / MCom (Risk Management), North-West University, Potchefstroom Campus, 2015

This paper examines the relationship between virtual currency, the Bitcoin, and the real economy. In the first part the description of the term virtual currency is provided with special focus on Bitcoin. Also the legal and taxation issues are discussed. In the main part the volatility of Bitcoin is inspected using various models from Autoregressive heteroskedasticity models family. We found that the volatility of Bitcoin differs significantly through time and that this relation is captured best by T-GARCH (1,1) model. Finally the relationship between Bitcoin and real economy indicators is observed to be inconsistent and mostly insignificant in time. Thus we conclude that the independency of Bitcoin cannot be rejected. Powered by TCPDF (www.tcpdf.org)

In this dissertation we proposed two generalizations of the Second-Order Least Squares (SLS) approach in two popular dynamic econometrics models. The first one is the regression model with time varying nonlinear mean function and autoregressive conditionally heteroskedastic (ARCH) disturbances. The second one is a linear dynamic panel data model. We used a semiparametric framework in both models where the SLS approach is based only on the first two conditional moments of response variable given the explanatory variables. There is no need to specify the distribution of the error components in both models. For the ARCH model under the assumption of strong-mixing process with finite moments of some order, we established the strong consistency and asymptotic normality of the SLS estimator. It is shown that the optimal SLS estimator, which makes use of the additional information inherent in the conditional skewness and kurtosis of the process, is superior to the commonly used quasi-MLE, and the efficiency gain is significant when the underlying distribution is asymmetric. Moreover, our large scale simulation studies showed that the optimal SLSE behaves better than the corresponding estimating function estimator in finite sample situation. The practical usefulness of the optimal SLSE was tested by an empirical example on the U.K. Inflation. For the linear dynamic panel data model, we showed that the SLS estimator is consistent and asymptotically normal for large N and finite T under fairly general regularity conditions. Moreover, we showed that the optimal SLS estimator reaches a semiparametric efficiency bound. A specification test was developed for the first time to be used whenever the SLS is applied to real data. Our Monte Carlo simulations showed that the optimal SLS estimator performs satisfactorily in finite sample situations compared to the first-differenced GMM and the random effects pseudo ML estimators. The results apply under stationary/nonstationary process and wih/out exogenous regressors. The performance of the optimal SLS is robust under near-unit root case. Finally, the practical usefulness of the optimal SLSE was examined by an empirical study on the U.S. airfares.

Durante os últimos anos, tem havido muitas mudanças na maneira como as instituições financeiras avaliam o risco. As regulações têm tido um papel muito importante no desenvolvimento das técnicas de medição do risco. Diante das diversidades de técnicas de estimação e análise de risco utilizadas pelas bolsas de valores e de futuros, nacionais e internacionais, bem como as Clearings de controle de risco, este estudo propôs uma análise comparativo de modelos de volatilidade para o cálculo do Value-at-Risk (VaR) aplicados aos principais índices de ações do mercado financeiro internacional. Utilizouse os modelos de volatilidade condicional da família ARCH levando em consideração a presença de longa dependência em seus retornos (memória longa) e assimetria na volatilidade. Em específico, utilizaram-se os modelos GARCH, EGARCH, APARCH, FIGARCH, FIEGARCH, FIAPARCH e HYGARCH estimados a parir de quatro diferentes distribuições, Normal, t-Student, G.E.D. e t-Student Assimétrica. Analisaramse os índices dos principais mercados de ações do mundo, sendo: Dow Jones, S&P 500, Nasdaq, Ibovespa, FTSE e Nikkei 225. Testou-se também a capacidade preditiva do modelo Riskmetrics desenvolvido pelo J.P. Morgan para o calculo do VaR, comparado com os modelos de volatilidade. Os resultados obtidos sugerem que o pacote desenvolvido pelo J.P.Morgan não se aplica adequadamente à realidade do mercado acionário mundial, como ferramenta de gestão e controle do risco das oscilações dos preços das ações de empresas negociadas nas bolsas de Nova Iorque, Nasdaq, BM&FBOVESPA, bolsa de Londres e bolsa de Tóquio. Os modelos que consideram o efeito de memória longa na volatilidade condicional dos retornos dos índices, em especial o modelo FIAPARCH (1,d,1), foram os que obtiveram melhor ajuste e desempenho preditivo do risco de mercado (Value-at-Risk), conforme valores apresentados pelo teste de razão de falha proposto por Kupiec (1995). / In recent years, there have been many changes in how financial institutions assess risk. The regulations have had a very important role in the development of techniques for measuring risk. Considering the diversity of estimation techniques and risk analysis used by stock exchanges and futures, national and international, as well as clearing houses of risk control, this study proposed a comparative analysis of volatility models for calculating Value-at-Risk (VaR) to the major stock indexes of international finance. It used models of conditional volatility of the ARCH family taking into account the presence of long dependence on their returns (long memory) and asymmetry in volatility. Specifically, it used the models GARCH, EGARCH, APARCH, FIGARCH, FIEGARCH, FIAPARCH and HYGARCH estimated the birth of four different distributions, Normal, t-Student, GED and t-Student Asymmetric. It analyzed the contents of the major stock markets of the world, being: Dow Jones, S & P 500, NASDAQ, Bovespa index, FTSE and Nikkei 225. Was also tested the predictive ability of the RiskMetrics model developed by JP Morgan for the calculation of VaR, compared with the models of volatility. The results suggest that the package developed by JPMorgan does not apply adequately to the reality of global stock market as a tool to manage and control the risk of fluctuations in stock prices of companies traded on the New York Stock Exchange, Nasdaq, BM&FBOVESPA, London Stock Exchange and Tokyo Stock Exchange. Models that consider the effect of long memory in conditional volatility of returns of the indices, especially the model FIAPARCH (1, d, 1), were the ones showing better fit and predictive performance of market risk (Value-at-Risk) , according to figures provided by the ratio test proposed by Kupiec (1995).

Made available in DSpace on 2015-05-08T14:44:44Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 1166218 bytes, checksum: 7fcb05d31169df50bbf76566f33a64de (MD5) Previous issue date: 2011-09-21 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / The objective is to achieve and suggest the inclusion of a financial indicator in the monetary policy rule that captures oscillations in capital markets, thereby promoting the flexibility of the inflation targeting system in order to preserve its effectiveness and transparency. It is argued that in periods of high volatility, the performance should be broader monitoring of financial assets in an attempt to avoid a process of asset deflation which led the economy into recession. The theoretical basis of this work is guided studies of Bernanke and Gertler (1999, 2000) that argue pro-introduction of a financial variable in the Taylor rule; the monetary policy should take into account the fluctuations in the stock market when they alter the forecast of future inflation. The models Vector autoregression (VAR) and extensions of the ARCH model will be addressed in order to justify the inclusion of the financial indicator in the system of inflation targets. It was observed that the volatility models presented persistence in the crisis period (2007-2009) for the financial variable while for the SELIC, the persistence of shocks has been lower intensity which implies that monetary policy may not be reacting properly variations in the financial market. For the VAR model, there was confirmation of the central hypothesis of the work since, in time of crisis, the effect on the financial indicator of the SELIC rate is higher compared to pre-crisis period. Therefore, the results support the hypothesis of Bernanke and Gertler (1999) that the Central Bank should consider the financial market only in times of high volatility, and clearly present their strategies and reports of communication with the market. / O objetivo é obter e sugerir a inclusão de um indicador financeiro na regra de política monetária que capte as oscilações no mercado de capitais, promovendo, assim, a flexibilização do regime de metas inflacionárias de forma a preservar a sua eficácia e transparência. Argumenta-se que em períodos de grande volatilidade, seja conveniente a atuação mais ampla no monitoramento dos ativos financeiros buscando evitar um processo de deflação de ativos que conduzisse a economia à recessão. A base teórica deste trabalho pauta-se nos estudos de Bernanke e Gertler (1999, 2000) que argumentam pró-introdução de uma variável financeira na Regra de Taylor; a política monetária deve levar em consideração as oscilações no mercado de capitais quando estas alteram a previsão de inflação futura. Os modelos de Vetores Auto-Regressivos (VAR) e extensões do modelo ARCH serão utilizados como forma de justificar a inclusão do indicador financeiro no sistema de metas inflacionárias. Observou-se que os modelos de volatilidade apresentaram persistência no período de crise (2007-2009) para a variável financeira enquanto que para a SELIC, a persistência dos choques tem sido em menor intensidade o que implica que a política monetária pode não estar reagindo adequadamente às variações no mercado financeiro. Para o modelo VAR, houve confirmação da hipótese central do trabalho visto que, no período de crise, o efeito do indicador financeiro sobre a SELIC é maior comparado ao período pré-crise. Portanto, os resultados apóiam a hipótese de Bernanke e Gertler (1999) de que o Banco Central deve levar em consideração o mercado financeiro apenas em momentos de grande volatilidade, e apresentar claramente suas estratégias e seus relatórios de comunicação com o mercado.

Durante os últimos anos, tem havido muitas mudanças na maneira como as instituições financeiras avaliam o risco. As regulações têm tido um papel muito importante no desenvolvimento das técnicas de medição do risco. Diante das diversidades de técnicas de estimação e análise de risco utilizadas pelas bolsas de valores e de futuros, nacionais e internacionais, bem como as Clearings de controle de risco, este estudo propôs uma análise comparativo de modelos de volatilidade para o cálculo do Value-at-Risk (VaR) aplicados aos principais índices de ações do mercado financeiro internacional. Utilizouse os modelos de volatilidade condicional da família ARCH levando em consideração a presença de longa dependência em seus retornos (memória longa) e assimetria na volatilidade. Em específico, utilizaram-se os modelos GARCH, EGARCH, APARCH, FIGARCH, FIEGARCH, FIAPARCH e HYGARCH estimados a parir de quatro diferentes distribuições, Normal, t-Student, G.E.D. e t-Student Assimétrica. Analisaramse os índices dos principais mercados de ações do mundo, sendo: Dow Jones, S&P 500, Nasdaq, Ibovespa, FTSE e Nikkei 225. Testou-se também a capacidade preditiva do modelo Riskmetrics desenvolvido pelo J.P. Morgan para o calculo do VaR, comparado com os modelos de volatilidade. Os resultados obtidos sugerem que o pacote desenvolvido pelo J.P.Morgan não se aplica adequadamente à realidade do mercado acionário mundial, como ferramenta de gestão e controle do risco das oscilações dos preços das ações de empresas negociadas nas bolsas de Nova Iorque, Nasdaq, BM&FBOVESPA, bolsa de Londres e bolsa de Tóquio. Os modelos que consideram o efeito de memória longa na volatilidade condicional dos retornos dos índices, em especial o modelo FIAPARCH (1,d,1), foram os que obtiveram melhor ajuste e desempenho preditivo do risco de mercado (Value-at-Risk), conforme valores apresentados pelo teste de razão de falha proposto por Kupiec (1995). / In recent years, there have been many changes in how financial institutions assess risk. The regulations have had a very important role in the development of techniques for measuring risk. Considering the diversity of estimation techniques and risk analysis used by stock exchanges and futures, national and international, as well as clearing houses of risk control, this study proposed a comparative analysis of volatility models for calculating Value-at-Risk (VaR) to the major stock indexes of international finance. It used models of conditional volatility of the ARCH family taking into account the presence of long dependence on their returns (long memory) and asymmetry in volatility. Specifically, it used the models GARCH, EGARCH, APARCH, FIGARCH, FIEGARCH, FIAPARCH and HYGARCH estimated the birth of four different distributions, Normal, t-Student, GED and t-Student Asymmetric. It analyzed the contents of the major stock markets of the world, being: Dow Jones, S & P 500, NASDAQ, Bovespa index, FTSE and Nikkei 225. Was also tested the predictive ability of the RiskMetrics model developed by JP Morgan for the calculation of VaR, compared with the models of volatility. The results suggest that the package developed by JPMorgan does not apply adequately to the reality of global stock market as a tool to manage and control the risk of fluctuations in stock prices of companies traded on the New York Stock Exchange, Nasdaq, BM&FBOVESPA, London Stock Exchange and Tokyo Stock Exchange. Models that consider the effect of long memory in conditional volatility of returns of the indices, especially the model FIAPARCH (1, d, 1), were the ones showing better fit and predictive performance of market risk (Value-at-Risk) , according to figures provided by the ratio test proposed by Kupiec (1995).

Changing in variance or volatility with time can be modeled as deterministic by using autoregressive conditional heteroscedastic (ARCH) type models, or as stochastic by using stochastic volatility (SV) models. This study compares these two kinds of models which are estimated on Turkish / USA exchange rate data. First, a GARCH(1,1) model is fitted to the data by using the package E-views and then a Bayesian estimation procedure is used for estimating an appropriate SV model with the help of Ox code. In order to compare these models, the LR test statistic calculated for non-nested hypotheses is obtained.

L'objectif de cette thèse est la construction des tests localement et asymptotiquement optimaux. Le problème traité concerne un modèle qui contient une large classe de modèles de séries chronologiques. La propriété de la normalité asymptotique locale (LAN) est l'outil fondamental utilisé dans nos travaux de recherches. Une application de nos travaux en finance est proposée / The purpose of this phD thesis is the construction of alocally asymptotically optimal tests. In this testing problem, the considered model contains a large class of time series models. LAN property was the fundamental tools in our research works. Our results are applied in financial area