Дисертації з теми "Generalized Autoregressive Conditional Heteroscedasticity"

The pandemic that struck the entire world 2020 caused by the SARS-CoV-2 (COVID-19) virus, will have an enormous interest for statistical and economical analytics for a long time. While the pandemic of 2020 is not the first that struck the entire world, it is the first pandemic in history where the data were gathered to this extent. Most countries have collected and shared its numbers of cases, tests and deaths related to the COVID-19 virus using different storage methods and different data types. Gaining quality data from the COVID-19 pandemic is a problem most countries had during the pandemic, since it is constantly changing not only for the current situation but also because past values have been altered when additional information has surfaced. The importance of having the latest data available for government officials to make an informed decision, leads to the usage of Business Intelligence tools and techniques for data gathering and aggregation being one way of solving the problem. One of the mostly used software to perform Business Intelligence is the Microsoft develop Power BI, designed to be a powerful visualizing and analysing tool, that could gather all data related to the COVID-19 pandemic into one application. The pandemic caused not only millions of deaths, but it also caused one of the largest drops on the stock market since the Great Recession of 2007. To determine if the deaths or other reasons directly caused the drop, the study modelled the volatility from index funds using Generalized Autoregressive Conditional Heteroscedasticity. One question often asked when talking of the COVID-19 virus, is how deadly the virus is. Analysing the effect the pandemic had on the mortality rate is one way of determining how the pandemic not only affected the mortality rate but also how deadly the virus is. The analysis of the mortality rate was preformed using Seasonal Artificial Neural Network. Forecasting deaths from the pandemic using the Seasonal Artificial Neural Network on the COVID-19 daily deaths data.

In this manuscript, I investigate the time-varying volatilities and co-volatilities in the fixed income and equities market using jump augmented stochastic volatility models. The results highlights that the fact that jumps are inherent in financial markets and have implications for the dynamics of volatilities and co-volatilities of financial assets over time. Jump augmented models provide a superior description of instantaneous market conditions and a promising avenue for future research in areas of asset pricing, portfolio selection, and risk management.

The main purpose of this thesis is to assess the potential of emerging stock markets and commodity markets in attracting the attention of international investors who utilize various portfolio diversification strategies to reduce the cumulative risk of their portfolio. A successful portfolio diversification strategy requires low correlation among financial markets. However, it is now well documented that the correlations among financial markets in developed countries are very high and hence the benefits of international portfolio diversification among these markets have been very limited. This fact suggests that investors should look for alternative markets whose correlations with developed markets are low (or even negative if possible) and which have high growth potentials. In this thesis, two emerging countries'
stock markets and two commodity markets are considered as alternative markets. Among emerging countries, Turkey and China are chosen due to their promising growth performance since the mid-2000s. As commodity markets, agricultural commodity and precious metal markets are selected because of the outstanding performance of the former and the "
safe harbor"
property of the latter. The structures and properties of dependence between these markets and stock markets in developed countries are examined by modeling the conditional correlation in the dynamic conditional correlation framework. The results reveal that upward trend hypothesis is valid for almost all correlations among market pairs and market volatility plays significant role in time varying structures of correlations.

In this dissertation, three essays are presented that apply recent advances in time-series methods to the analysis of inflation and stock market index data for Taiwan. Specifically, ARCH and GARCH methodologies are used to investigate claims of increased volatility in economic time-series data since 1980. In the first essay, analysis that accounts for structural change reveals that the fundamental relationship between inflation and its variability was severed by policies implemented during economic liberalization in Taiwan in the early 1980s. Furthermore, if residuals are corrected for serial correlation, evidence in favor of ARCH effects is weakened. In the second essay, dynamic linkages between daily stock returns and daily trading volume are explored. Both linear and nonlinear dependence are evaluated using Granger causality tests and GARCH modelling. Results suggest significant unidirectional Granger causality from stock returns to trading volume. In the third essay, comparative analysis of the frequency structure of the Taiwan stock index data is conducted using daily, weekly, and monthly data. Results demonstrate that the relationship between mean return and its conditional standard deviation is positive and significant only for high-frequency daily data.

O padrão espacial de ocorrência de atributos de espécies florestais, tal como a área basal das árvores, pode fornecer informações para o entendimento da estrutura da comunidade vegetal. Uma vez que fatores ambientais podem influenciar tanto o padrão espacial de ocorrência quanto os atributos das espécies em florestas nativas. Desse modo, investigar a relação entre as características ambientais e o padrão espacial de espécies florestais pode ajudar a entender a dinâmica das florestas. Especificamente, neste trabalho, o objetivo é avaliar métodos estatísticos que permitam identificar quais atributos do solo são capazes de explicar a variação da área basal de cada espécie de árvore. A área basal foi considerada como variável resposta e como covariáveis, um grande número de atributos físicos e químicos do solo, medidos em uma malha de localizações cobrindo a área de estudo. Foram revisados e utilizados os métodos de regressão linear múltipla com método de seleção stepwise, modelos aditivos generalizados e árvores de regressão. Em uma segunda fase das análises, adicionou-se um efeito espacial aos modelos, com o intuito de verificar se havia ainda padrões na variabilidade, não capturados pelos modelos. Com isso, foram considerados os modelos autoregressivo simultâneo, condicional autoregressivo e geoestatístico. Dado o grande número de atributos do solo, as análises foram também conduzidas utilizando-se as covariáveis originais, fatores identificados em uma análise fatorial prévia dos atributos de solo. A seleção de modelos com melhor ajuste foi utilizada para identificar os atributos de solo relevantes, bem como a presença e melhor descrição de padrões espaciais. A área de estudo foi a Estação Ecológica de Assis, da Unidade de Conservação do Estado de São Paulo em parcelas permanentes, dentro do projeto \"Diversidade, Dinâmica e Conservação em Florestas do Estado de São Paulo: 40 ha de parcelas permanentes\", do programa Biota da FAPESP. As análises reportadas aqui se referem à área basal das espécies Copaifera langsdorffii, Vochysia tucanorum e Xylopia aromatica. Com os atributos de solo reduzidos e consistentemente associados à área basal, a declividade, altitude, saturação por alumínio e potássio mostraram-se relevantes para duas das espécies. Resultados obtidos mostraram a presença de um padrão na variabilidade, mesmo levando-se em consideração os efeitos das covariáveis, ou seja, os atributos do solo explicam parcialmente a variabilidade da área basal, mas existe um padrão que ocorre no espaço que não é capturado por essas covariáveis.
The spatial pattern of occurrenceis of forest species and their attributes, such as the basal area of trees, can provide information for understanding the structure of the vegetable community. Considering the environmental factors can influence the spatial pattern of occurrences of species in native forests and related attributes, describing relationship between environmental characteristics and spatial pattern of forest species can be associated with the dynamics of forests. The objective of the present study is to assess different statistical methods used to identify which soil attributes are associated with the basal area of each tree selected species. The basal area was considered as the response variable and the covariates are given by a large number of physical and chemical attributes of the soil, measured at a grid of locations covering the study area. The methods considered are the multiple linear regression with stepwise model selection, generalized additive models and regression trees. Spatial effects were added to the models, in order to ascertain whether there is residual spatial patterns not captured by the covariates. Thus, simultaneous autoregressive model, autoregressive conditional and geostatistical were considered. Considering the large number of soil attributes, analysis were were conducted both ways, using the original covariates, and using factors identified in a preliminar factor analysis of the soil attributes. Model selection was used to identify the relevant attributes of soil as well as the presence and better description of spatial patterns. The study area was the Ecological Station of Assis, the Conservation Unit of the State of São Paulo in permanent plots within the \"Diversity Dynamics and Conservation Forests in the State of São Paulo: 40 ha of permanent plots\" project, under the research project FAPESP biota. The analyzes reported here refer to the basal area of the species Copaifera langsdorffii, Vochysia tucanorum and Xylopia aromatica. Results differ among the considered methods reinforcing the reccomendation of considering differing modeling strategies. Covariates consistently associated with basal area are slope, altitude and aluminum saturation, potassium, relevant to at least two of the species. Results obtained showed the presence of patterns in residual variability, even taking into account the effects of covariates. The soil characteristics only partially explain the variability of the basal area and there are spatial patterns not captured by these covariates.

This study has applied a geographical perspective with the ambition of evaluating the presence of the Sell in May effect, January effect and monthly anomalies in the Nordic stock markets. In extension the study examines the relationship between corporate size and the returns of calendar anomalies. The study has conducted statistical tests based on Newey-West regressions as well as a Generalized Auto-Regressive Conditional Heteroscedasticity model. The findings suggest that the Sell in May and January are present in the Nordic region and partially abide by theory and results of previous research. The findings suggest that the Sell in May and January effect are independent, however, tendencies when the January effect has a considerable influence on the Sell in May effect are also evident. Additionally, the “April Effect” is an unexpected outlier with positive excess returns that was identified through this study.

We investigate some simulation-based approaches for the valuing of the employee stock options. The mathematical models that deal with valuation of such options include the work of Jennergren and Naeslund [L.P Jennergren and B. Naeslund, A comment on valuation of executive stock options and the FASB proposal, Accounting Review 68 (1993) 179-183]. They used the Black and Scholes [F. Black and M. Scholes, The pricing of options and corporate liabilities, Journal of Political Economy 81(1973) 637-659] and extended partial differential equation for an option that includes the early exercise. Some other major relevant works to this mini thesis are Hemmer et al. [T Hemmer, S. Matsunaga and T Shevlin, The influence of risk diversification on the early exercise of employee stock options by executive officers, Journal of Accounting and Economics 21(1) (1996) 45-68] and Baril et al. [C. Baril, L. Betancourt, J. Briggs, Valuing employee stock options under SFAS 123 R using the Black-Scholes-Merton and lattice model approaches, Journal of Accounting Education 25 (1-2) (2007) 88-101]. The underlying assets are studied under the GARCH (generalized autoregressive conditional heteroskedasticity) effects. Particular emphasis is made on the American style employee stock options.

Nessa tese apresentamos três diferentes aplicações dos modelos Birnbaum-Saunders. No capítulo 2 introduzimos um novo método por função-núcleo não-paramétrico para a estimação de densidades assimétricas, baseado nas distribuições Birnbaum-Saunders generalizadas assimétricas. Funções-núcleo baseadas nessas distribuições têm a vantagem de fornecer flexibilidade nos níveis de assimetria e curtose. Em adição, os estimadores da densidade por função-núcleo Birnbaum-Saunders gene-ralizadas assimétricas são livres de viés na fronteira e alcançam a taxa ótima de convergência para o erro quadrático integrado médio dos estimadores por função-núcleo-assimétricas-não-negativos da densidade. Realizamos uma análise de dados consistindo de duas partes. Primeiro, conduzimos uma simulação de Monte Carlo para avaliar o desempenho do método proposto. Segundo, usamos esse método para estimar a densidade de três dados reais da concentração de poluentes atmosféricos. Os resultados numéricos favorecem os estimadores não-paramétricos propostos. No capítulo 3 propomos uma nova família de modelos autorregressivos de duração condicional baseados nas distribuições misturas de escala Birnbaum-Saunders (SBS). A distribuição Birnbaum-Saunders (BS) é um modelo que tem recebido considerável atenção recentemente devido às suas boas propriedades. Uma extensão dessa distribuição é a classe de distribuições SBS, a qual (i) herda várias das boas propriedades da distribuição BS, (ii) permite a estimação de máxima verossimilhança em uma forma eficiente usando o algoritmo EM, e (iii) possibilita a obtenção de um procedimento de estimação robusta, entre outras propriedades. O modelo autorregressivo de duração condicional é a família primária de modelos para analisar dados de duração de transações de alta frequência. A metodologia estudada aqui inclui estimação dos parâmetros pelo algoritmo EM, inferência para esses parâmetros, modelo preditivo e uma análise residual. Realizamos simulações de Monte Carlo para avaliar o desempenho da metodologia proposta. Ainda, avalia-mos a utilidade prática dessa metodologia usando dados reais de transações financeiras da bolsa de valores de Nova Iorque. O capítulo 4 trata de índices de capacidade do processo (PCIs), os quais são ferramentas utilizadas pelas empresas para determinar a qualidade de um produto e avaliar o desempenho de seus processos de produção. Estes índices foram desenvolvidos para processos cuja característica de qualidade tem uma distribuição normal. Na prática, muitas destas ca-racterísticas não seguem esta distribuição. Nesse caso, os PCIs devem ser modificados considerando a não-normalidade. O uso de PCIs não-modificados podemlevar a resultados inadequados. De maneira a estabelecer políticas de qualidade para resolver essa inadequação, transformação dos dados tem sido proposta, bem como o uso de quantis de distribuições não-normais. Um distribuição não-normal assimétrica o qual tem tornado muito popular em tempos recentes é a distribuição Birnbaum-Saunders (BS). Propomos, desenvolvemos, implementamos e aplicamos uma metodologia baseada em PCIs para a distribuição BS. Além disso, realizamos um estudo de simulação para avaliar o desempenho da metodologia proposta. Essa metodologia foi implementada usando o software estatístico chamado R. Aplicamos essa metodologia para um conjunto de dados reais de maneira a ilustrar a sua flexibilidade e potencialidade.
In this thesis, we present three different applications of Birnbaum-Saunders models. In Chapter 2, we introduce a new nonparametric kernel method for estimating asymmetric densities based on generalized skew-Birnbaum-Saunders distributions. Kernels based on these distributions have the advantage of providing flexibility in the asymmetry and kurtosis levels. In addition, the generalized skew-Birnbaum-Saunders kernel density estimators are boundary bias free and achieve the optimal rate of convergence for the mean integrated squared error of the nonnegative asymmetric kernel density estimators. We carry out a data analysis consisting of two parts. First, we conduct a Monte Carlo simulation study for evaluating the performance of the proposed method. Second, we use this method for estimating the density of three real air pollutant concentration data sets, whose numerical results favor the proposed nonparametric estimators. In Chapter 3, we propose a new family of autoregressive conditional duration models based on scale-mixture Birnbaum-Saunders (SBS) distributions. The Birnbaum-Saunders (BS) distribution is a model that has received considerable attention recently due to its good properties. An extension of this distribution is the class of SBS distributions, which allows (i) several of its good properties to be inherited; (ii) maximum likelihood estimation to be efficiently formulated via the EM algorithm; (iii) a robust estimation procedure to be obtained; among other properties. The autoregressive conditional duration model is the primary family of models to analyze high-frequency financial transaction data. This methodology includes parameter estimation by the EM algorithm, inference for these parameters, the predictive model and a residual analysis. We carry out a Monte Carlo simulation study to evaluate the performance of the proposed methodology. In addition, we assess the practical usefulness of this methodology by using real data of financial transactions from the New York stock exchange. Chapter 4 deals with process capability indices (PCIs), which are tools widely used by companies to determine the quality of a product and the performance of their production processes. These indices were developed for processes whose quality characteristic has a normal distribution. In practice, many of these characteristics do not follow this distribution. In such a case, the PCIs must be modified considering the non-normality. The use of unmodified PCIs can lead to inadequacy results. In order to establish quality policies to solve this inadequacy, data transformation has been proposed, as well as the use of quantiles from non-normal distributions. An asymmetric non-normal distribution which has become very popular in recent times is the Birnbaum-Saunders (BS) distribution. We propose, develop, implement and apply a methodology based on PCIs for the BS distribution. Furthermore, we carry out a simulation study to evaluate the performance of the proposed methodology. This methodology has been implemented in a noncommercial and open source statistical software called R. We apply this methodology to a real data set to illustrate its flexibility and potentiality.

M.Com. (Economic Development and Policy Issues)
This research analyses the effect of exchange rate volatility on exports using a sample of nine emerging countries – Argentina, Brazil, India, Indonesia, Mexico, Malaysia, Poland, South Africa and Thailand – between 1995 and 2010. The study uses panel data models, with a standard exports equation with exports performance determined by exchange rate volatility, the level of exchange rate, demand conditions in major countries as well as terms of trade. Exchange rate volatility is measured by Generalised Autoregressive Conditional Heteroscedasticity (GARCH) and conventional standard deviation in order to determine if the instrument of volatility used influences the nature of the relationship between exchange rate volatility and exports. The results show that exchange rate volatility has a significant negative effect on the performance of exports regardless of the measure of volatility used. The Pedroni residual cointegration method was used to test for panel cointegration to determine if there is a long-run relationship among the variables, and the test showed that a long-run relationship does exists. Generally, the study concludes that policy mix that will reduce exchange rate volatility (such as managed exchange rate regimes) and relatively competitive exchange rates are essential for emerging markets in order to sustain their exports performance.

碩士
國立中興大學
應用數學系所
94
The growth curve model that the covariance matrix constructed with autoregressive (AR) dependence of degree 1 and autoregressive conditional heteroscedasiticity (ARCH) of degree 1 is studied in the thesis. The specification of the multivariate normal distribution with these two properties is dedicated. I consider both maximum likelihood inference perspective and Bayesian inference perspective for estimation and prediction. An algorithm is introduced for determining maximum likelihood estimates of the unknown parameters, on the other hand, Markov Chain Monte Carlo methods are elaborated for Bayesian estimation and prediction. The forms of the condictional predictor and extended predictor are provided and illustrated with numerical results of both real data and simulated data

The thesis investigates relationship between daily stock return volatility of Dow Jones Industrial Average stocks and data obtained on Twitter, the social media network. The Twitter data set contains a number of tweets, categorized according to their polarity, i.e. positive, negative and neutral sentiment of tweets. We construct two classes of models, GARCH and ARFIMA, where for either of them we research basic model setting and setting with additional Twitter variables. Our goal is to compare, which of them predicts the one day ahead volatility most precisely. Besides, we provide commentary regarding the effects of Twitter volume variables on future stock volatility. The analysis has revealed that the best performing model, given the length and structure of our data set, is the ARFIMA model augmented on Twitter volume residuals. In the context of the thesis, Twitter volume residuals represent unexpected activity on the social media network and are obtained as residuals from Twitter volume autoregression. Plain ARFIMA model was the second best and plain volume augmented ARFIMA was in third place. This means that all three ARFIMA models outperformed all three GARCH models in our research. Regarding the Twitter estimation parameters, we found that higher the activity the higher tomorrow's stock...

碩士
淡江大學
國際貿易學系
88
(G)ARCH modeling with a leptokurtic distribution has been found useful to account for the condition heterscedasticity and leptokurtosis , but it can''t accommodate other commonly observed stylized effects in high frequency data, like peakedness and skewness. Wang etal (2000) proposed a very general and flexible GARCH-EGB2 model which can accommodate more data characteristics, such as asymmetry, high peakedness, volatility clustering and leptokurtosis. In this paper, we further extended Wang etal''s work to allow the shape parameters following the structure of Hansen''s autoregressive conditional density model (ARCD, 1994). In our framework, the higher order moments ( skewness and kurtosis) could be time varying functions of the conditioning information rather than constant over time. Since the higher order moments provide important insights of particular interest to investors, a more complete understanding of both characteristics have the potential to alter optimal risk management strategy. Therefore, another innovation in this paper is to extend the GARCH-in-mean model by explicitly modeling the influence of three conditional moments ( conditional variance, conditional skewness, conditional kurtosis ) on the conditional expectation of the data series. Applied to Taiwan stock returns data, empirical results suggest a preponderance of evidence to support the time varying moments in mean model specification over competing alternatives.

This study investigates the return generating process underlying the South African stock market. The investigation of the return generating process is framed within the Arbitrage Pricing Theory (APT) framework with the APT reinterpreted so as to provide a conceptual framework within which the return generating process can be investigated. In modelling the return generating process, the properties of South African stock returns are taken into consideration and an appropriate econometric framework in the form of Autoregressive Conditional Heteroscedastic (ARCH) and Generalized Autoregressive Conditional Heteroscedastic (GARCH) models is applied. Results indicate that the return generating process of South African stock returns is described by innovations in multiple risk factors representative of several risk categories. The multifactor model of the return generating process explains a substantial amount of variation in South African stock returns and the ARCH/GARCH methodology is an appropriate econometric framework for the estimation of models of the return generating process. The APT framework is successfully applied to model and investigate the return generating process of South African stock returns.