This paper surveys various statistical methods that have been proposed for the examination of the efficiency of financial markets and proposes a novel procedure for testing the predictability of a time series. For illustration, this procedure is applied to Austrian stock return series.

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...

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.

Value at Risk has over the last couple of decades become one of the most widely used measures of market risk. Several methods to compute this measure have been suggested. In this paper, we evaluate the use of the GARCH(1,1)-, EGARCH(1,1)- and the APARCH(1,1) model for estimation of this measure under the assumption that the conditional error distribution is normally-, t-, skewed t- and NIG-distributed respectively. For each model, the 95% and 99% one-day Value at Risk is computed using rolling out-of-sample forecasts for three equity indices. These forecasts are evaluated with Kupiec´s test for unconditional coverage test and Christoffersen’s test for conditional coverage. The results imply that the models generally perform well. The APARCH(1,1) model seems to be the most robust model. However, the GARCH(1,1) and the EGARCH(1,1) models also provide accurate predictions. The results indicate that the assumption of conditional distribution matters more for 99% than 95% Value at Risk. Generally, a leptokurtic distribution appears to be a sound choice for the conditional distribution.

Modelos GARCH tendo a normal e a t-Student como distribuições condicionais são amplamente utilizados para modelagem da volatilidade de dados financeiros. No entanto, tais distribuições podem não ser apropriadas para algumas séries com caudas pesadas e comportamento leptocúrtico. As chamadas distribuições estáveis podem ser mais adequadas para sua modelagem, como já explorado na literatura. Por outro lado, os modelos GAS (Generalized Autoregressive Score), com desenvolvimento recente, tratam-se de modelos dinâmicos que possuem em sua estrutura a função score (derivada do logaritmo da verossimilhança). Tal abordagem oferece uma direção natural para a evolução dos parâmetros da distribuição dos dados. Neste trabalho, é proposto um novo modelo GAS em conjunção com distribuições estáveis simétricas para a modelagem da volatilidade - de fato, é uma generalização do GARCH, pois, para uma particular escolha de distribuição estável e de estrutura do modelo, tem-se o clássico modelo GARCH gaussiano. Como em geral a função densidade das distribuições estáveis não possui forma analítica fechada, é apresentado seu procedimento de cálculo, bem como de suas derivadas, para o completo desenvolvimento do método de estimação dos parâmetros. Também são analisadas as condições de estacionariedade e a estrutura de dependência do modelo. Estudos de simulação são conduzidos, bem como uma aplicação a dados reais, para comparação entre modelos usuais, que utilizam distribuições normal e t-Student, e o modelo proposto, demonstrando a eficácia deste. / GARCH models with normal and t-Student conditional distributions are widely used for volatility modeling in financial data. However, such distributions may not be suitable for some heavy-tailed and leptokurtic series. The stable distributions may be more adequate to fit such characteristics, as already exploited in the literature. On the other hand, the recently developed GAS (Generalized Autoregressive Score) models are dynamic models in which the updating mechanism of the time-varying parameters is based on the score function (first derivative of the log-likelihood function). This provides the natural direction for updating the parameters, based on the complete density. We propose a new GAS model with symmetric stable distribution for volatility modeling. The model can be interpreted as a generalization of the GARCH models, since the classic gaussian GARCH model is derived from it by using particular choices of the stable distribution and the model structure. There are no closed analytical expressions for general stable densities in most cases, hence its numeric computation and derivatives are detailed for the sake of complete development of the estimation process. The stationarity conditions and the dependence structure of the model are analysed. Simulation studies, as well as an application to real data, are presented for comparisons between the usual models and the proposed model, illustrating the effectiveness of the latter.

Modelos GARCH tendo a normal e a t-Student como distribuições condicionais são amplamente utilizados para modelagem da volatilidade de dados financeiros. No entanto, tais distribuições podem não ser apropriadas para algumas séries com caudas pesadas e comportamento leptocúrtico. As chamadas distribuições estáveis podem ser mais adequadas para sua modelagem, como já explorado na literatura. Por outro lado, os modelos GAS (Generalized Autoregressive Score), com desenvolvimento recente, tratam-se de modelos dinâmicos que possuem em sua estrutura a função score (derivada do logaritmo da verossimilhança). Tal abordagem oferece uma direção natural para a evolução dos parâmetros da distribuição dos dados. Neste trabalho, é proposto um novo modelo GAS em conjunção com distribuições estáveis simétricas para a modelagem da volatilidade - de fato, é uma generalização do GARCH, pois, para uma particular escolha de distribuição estável e de estrutura do modelo, tem-se o clássico modelo GARCH gaussiano. Como em geral a função densidade das distribuições estáveis não possui forma analítica fechada, é apresentado seu procedimento de cálculo, bem como de suas derivadas, para o completo desenvolvimento do método de estimação dos parâmetros. Também são analisadas as condições de estacionariedade e a estrutura de dependência do modelo. Estudos de simulação são conduzidos, bem como uma aplicação a dados reais, para comparação entre modelos usuais, que utilizam distribuições normal e t-Student, e o modelo proposto, demonstrando a eficácia deste. / GARCH models with normal and t-Student conditional distributions are widely used for volatility modeling in financial data. However, such distributions may not be suitable for some heavy-tailed and leptokurtic series. The stable distributions may be more adequate to fit such characteristics, as already exploited in the literature. On the other hand, the recently developed GAS (Generalized Autoregressive Score) models are dynamic models in which the updating mechanism of the time-varying parameters is based on the score function (first derivative of the log-likelihood function). This provides the natural direction for updating the parameters, based on the complete density. We propose a new GAS model with symmetric stable distribution for volatility modeling. The model can be interpreted as a generalization of the GARCH models, since the classic gaussian GARCH model is derived from it by using particular choices of the stable distribution and the model structure. There are no closed analytical expressions for general stable densities in most cases, hence its numeric computation and derivatives are detailed for the sake of complete development of the estimation process. The stationarity conditions and the dependence structure of the model are analysed. Simulation studies, as well as an application to real data, are presented for comparisons between the usual models and the proposed model, illustrating the effectiveness of the latter.

Title: Selected problems of financial time series modelling Author: Radek Hendrych Department: Department of Probability and Mathematical Statistics (DPMS) Supervisor: Prof. RNDr. Tomáš Cipra, DrSc., DPMS Abstract: The present dissertation thesis deals with selected problems of financial time series analysis. In particular, it focuses on two fundamental aspects of condi- tional heteroscedasticity modelling. The first part of the thesis introduces and discusses self-weighted recursive estimation algorithms for several classic univariate conditional heteroscedasticity models, namely for the ARCH, GARCH, RiskMetrics EWMA, and GJR-GARCH processes. Their numerical capabilities are demonstrated by Monte Carlo experiments and real data examples. The second part of the thesis proposes a novel approach to conditional covariance (correlation) modelling. The suggested modelling technique has been inspired by the essential idea of the multivariate orthogonal GARCH method. It is based on a suitable type of linear time-varying orthogonal transformation, which enables to employ the constant conditional correlation scheme. The correspond- ing model is implemented by using a nonlinear discrete-time state space representation. The proposed approach is compared with other commonly applied models. It demon- strates its...

This thesis focuses on analysis and comparison of volatility on selected European stock markets. At first paper briefly introduces the reader to the specific features of financial econometrics and the importance of asset returns volatility analysis. Further chapters precisely cover the construction of linear and nonlinear conditional heteroscedasticity models as an appropriate tool for describing the volatility in financial data. The empirical part of the thesis analyze four stock exchange indices from various European regions and seek appropriate models to express volatility behavior in period before the financial crisis in 2008 and also during the crisis phase. Based on selected models, the paper tries to compare the volatility in both periods within the specific stock market index and moreover between different regions. The last section examines asymmetric effects in volatility of stock indices using their graphical representation.

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.

Darbe siekiama aprašyti periodinį ilgos atminties finansinių laiko eilučių elgesį. Remiantis anksčiau sukurtais modeliais, siūlomas h-faktorių Gegenbauer-LARCH modelis, kuris į LARCH tipo proceso sąlyginės dispersijos lygtį įtraukia apibendrintą ilgos atminties filtrą, paremtą Gegenbauer polinomais. Darbe pateikiama anksčiau sukurtų modelių, skirtų finansinių aktyvų grąžų kintamumo modeliavimui, apžvalga. Remiantis ankstesnėmis idėjomis ir darbais, sukonstruojamas naujas Gegenbauer-LARCH modelis, kuriam tikrinama kovariacijos stacionarumo sąlyga. Pateikiamos modeliuotos h-faktorių Gegenbauer-LARCH proceso trajektorijos. Sukurtas modelis taikomas realiems Euro-Dolerio valiutų kurso duomenims. Identifikuotas modelio parametrai vertinami LUDE algoritmu, kuris maksimizuoja didžiausio tikėtinumo funkciją. Atliekama modelio adekvatumo analizė. Darbo pabaigoje pateikiamos išvados ir rekomendacijos. / On the ground of previous works and ideas a new class of models which describe long memory periodic behaviour in a time varying volatility of financial returns is introduced. Generalised periodic long-memory filters, based on Gegenbauer polynomials, are included into volatility equation of LARCH model and capture long memory periodic behaviour of the data. Thus, a new type of model called h-factor Gegenbauer-LARCH is presented. Moreover, a covariance stationarity condition is checked for one factor Gegenbauer-LARCH model. Also, generated processes are demonstrated. Furthermore, h-factor Gegenbauer-LARCH model is applied to Euro-Dollar hourly exchange rate returns. Identified model is estimated by means of LUDE algorithm which maximizes maximum likelihood function. The adequasy of the model is checked by reviewing residuals behaviour. Concerning empirical results the following conclusion is drawn: • Although model captures specific characteristics of the data such as slowly decaying periodic behaviour of autocorrelation function and pronounced peaks in periodogram but residuals analysis shows that model should be improved. Bordignon, Caporin, Lisi suggest that all possible frequencies were included to the model because higher frequencies might not be obvious from autocorrelation function or periodogram. However, we face computer capability problem. As a matter of fact, we cannot estimate a more complex model. Inclusion of autoregresive coefficients into the model did not... [to full text]