<p>In this paper we aim to investigate volatility and correlation of sector</p><p>indexes of Nordic Market. More precisely we work with OMX Stockholm</p><p>Exchange Indexes, considering the Paper, the Energy and the Bank</p><p>sectors.</p><p>We use daily returns over the period from 5 January 2001 to 13 April</p><p>2007 and compute and forecast return volatility using the GARCH(1; 1)</p><p>model. We also calculate the correlation matrix of the indexes.</p><p>The GARCH(1; 1) model ¯t the empirical data well for all three sectors</p><p>and can therefore be used for volatility forecasts. Here, we have pre-</p><p>dicted the one-day-ahead forecasts and based on these data calculated</p><p>the correlation matrix. The results from these calculations show that</p><p>all three sectors are highly correlated. We obtained however the small-</p><p>est correlation between Paper and Energy which was surprising as the</p><p>Paper industry is very energy consuming. This result indicates other</p><p>relations between Paper and Energy.</p>

In this paper we aim to investigate volatility and correlation of sector indexes of Nordic Market. More precisely we work with OMX Stockholm Exchange Indexes, considering the Paper, the Energy and the Bank sectors. We use daily returns over the period from 5 January 2001 to 13 April 2007 and compute and forecast return volatility using the GARCH(1; 1) model. We also calculate the correlation matrix of the indexes. The GARCH(1; 1) model ¯t the empirical data well for all three sectors and can therefore be used for volatility forecasts. Here, we have pre- dicted the one-day-ahead forecasts and based on these data calculated the correlation matrix. The results from these calculations show that all three sectors are highly correlated. We obtained however the small- est correlation between Paper and Energy which was surprising as the Paper industry is very energy consuming. This result indicates other relations between Paper and Energy.

This paper considers the high-moments and uses the skew generalized error distribution (SGED) to explain the financial market data which have leptokurtic, fat-tailed and skewness. And we compare performance with the commonly used symmetrical distribution model such as normal distribution, student¡¦s t distribution and generalized error distribution (GED). To research when returns of asset have leptokurtic and fat-tailed phenomena, what model has better predictive power for volatility forecasting? The empirical procedure is as follows: First step, make the descriptive statistics of raw data, and know that the GARCH effect should be considered, followed by selecting the optimal order of ARMA-GARCH. The second steps, make the parameter estimations of full-sample, and pick up the best model. Finally, forecast out-of-sample volatility for 1-day, 2-day, 5-day, 10-day and 20-day respectively, not only use different loss function to measure the performance, but also use DM test to compare the relative predictive power of the models under the different error distribution.

Made available in DSpace on 2010-04-20T20:22:19Z (GMT). No. of bitstreams: 1 66070100189.pdf: 307836 bytes, checksum: 73f8a3fbe747a93cdaf1f9a937909e1e (MD5) Previous issue date: 2010-01-28T00:00:00Z / O objetivo desse trabalho é avaliar a capacidade de previsão do mercado sobre a volatilidade futura a partir das informações obtidas nas opções de Petrobras e Vale, além de fazer uma comparação com modelos do tipo GARCH e EWMA. Estudos semelhantes foram realizados no mercado de ações americano: Seja com uma cesta de ações selecionadas ou com relação ao índice S&P 100, as conclusões foram diversas. Se Canina e Figlewski (1993) a 'volatilidade implícita tem virtualmente nenhuma correlação com a volatilidade futura', Christensen e Prabhala (1998) concluem que a volatilidade implícita é um bom preditor da volatilidade futura. No mercado brasileiro, Andrade e Tabak (2001) utilizam opções de dólar para estudar o conteúdo da informação no mercado de opções. Além disso, comparam o poder de previsão da volatilidade implícita com modelos de média móvel e do tipo GARCH. Os autores concluem que a volatilidade implícita é um estimador viesado da volatilidade futura mas de desempenho superior se comparada com modelos estatísticos. Gabe e Portugal (2003) comparam a volatilidade implícita das opções de Telemar (TNLP4) com modelos estatísticos do tipo GARCH. Nesse caso, volatilidade implícita tambem é um estimador viesado, mas os modelos estatísticos além de serem bons preditores, não apresentaram viés. Os dados desse trabalho foram obtidos ao longo de 2008 e início de 2009, optando-se por observações intradiárias das volatilidades implícitas das opções 'no dinheiro' de Petrobrás e Vale dos dois primeiros vencimentos. A volatidade implícita observada no mercado para ambos os ativos contém informação relevante sobre a volatilidade futura, mas da mesma forma que em estudos anteriores, mostou-se viesada. No caso específico de Petrobrás, o modelo GARCH se mostrou um previsor eficiente da volatilidade futura / The purpose of this study is to examine the predictive power of the market about future volatility using the information obtained from the options on Petrobras and Vale. We will also compare the results with models such as GARCH and EWMA. Similar studies were performed in the U.S. stock market: Either with selected stocks or the S & P 100 Index, the results are not conclusive. Even if Canina and Figlewski (1993) find that the "implied volatility has virtually no correlation with future volatility”, Christensen and Prabhala (1998) conclude that implied volatility is a good predictor of future volatility. Andrade and Tabak (2001) use dollar options to study the information content power of the options on dollar. They also compare the predictive power of implied volatility with models such as EWMA or GARCH. The authors conclude that implied volatility is a biased estimator of future volatility but has a better performance compared with statistical models. Gabe and Portugal (2003) compare the implied volatility of options on Telemar (TNLP4) with statistical models like GARCH. In this case, implied volatility is also a biased estimator, but the statistical models were also good predictors and showed no bias. The data in this study are taken during 2008 and early 2009, using intraday observations of implied volatilities for the first two maturities of "at the money" options on Petrobras and Vale. The observed implied volatility for both stocks contains relevant information about future volatility,similarly to previous studies, is biased. Specifically for Petrobras, GARCH model proved to be an efficient predictor of future volatility.

Submitted by (ana.araujo@ufrpe.br) on 2016-08-04T15:54:10Z No. of bitstreams: 1 Marcela Veronica Alves de Souza.pdf: 493032 bytes, checksum: 61ed79a4b91e6c9460233f6b3ab961d2 (MD5) / Made available in DSpace on 2016-08-04T15:54:10Z (GMT). No. of bitstreams: 1 Marcela Veronica Alves de Souza.pdf: 493032 bytes, checksum: 61ed79a4b91e6c9460233f6b3ab961d2 (MD5) Previous issue date: 2005-02-28 / The main aim of the present dissertation is to present a modeling methodology and forecast of the volatility of the Arabic coffee, with the intent not only to predict and explain its conditional heteroskedasticity, but also to obtain the market risk for its investments. For modeling and prevision of volatility in this dissertation, the temporal series of Arabic coffee returns from September 1996 to December 2004, was used. The ARIMA models were analyzed, together with non-linear ARCH models, and their generalization GARCH. The results predict high volatility and investment loss for up to nine steps ahead. The results also indicate that the GARCH model, adjusted to the residuals of the AR model, presents the largest forecast power one step ahead / O principal objetivo da presente dissertação é apresentar uma metodologia de modelagem e previsão da volatilidade do café Arábica, com o intuito não só de explicar e prever sua heteroscedasticidade condicional, como de obter o risco de mercado para seus investimentos. Ao longo desta dissertação trabalhamos com a série temporal dos retornos diários do café Arábica de setembro de 1996 a dezembro de 2004 para modelagem e previsão da volatilidade. Analisamos os modelos ARIMA, assim como utilizamos os modelos não -lineares ARCH e sua generalização, GARCH. Contudo, os resultados preveem alta volatilidade e perda nos investimentos para até nove passos à frente. Estes resultados também revelam o modelo GARCH ajustado aos resíduos de um modelo AR, dentre os modelos considerados, como o modelo de maior poder preditivo, um passo à frente.

<p>This doctoral thesis is comprised of four papers that all relate to the subject of Time Series Analysis.</p><p>The first paper of the thesis considers point estimation in a nonnegative, hence non-Gaussian, AR(1) model. The parameter estimation is carried out using a type of extreme value estimators (EVEs). A novel estimation method based on the EVEs is presented. The theoretical analysis is complemented with Monte Carlo simulation results and the paper is concluded by an empirical example.</p><p>The second paper extends the model of the first paper of the thesis and considers semiparametric, robust point estimation in a nonlinear nonnegative autoregression. The nonnegative AR(1) model of the first paper is extended in three important ways: First, we allow the errors to be serially correlated. Second, we allow for heteroskedasticity of unknown form. Third, we allow for a multi-variable mapping of previous observations. Once more, the EVEs used for parameter estimation are shown to be strongly consistent under very general conditions. The theoretical analysis is complemented with extensive Monte Carlo simulation studies that illustrate the asymptotic theory and indicate reasonable small sample properties of the proposed estimators.</p><p>In the third paper we construct a simple nonnegative time series model for realized volatility, use the results of the second paper to estimate the proposed model on S&P 500 monthly realized volatilities, and then use the estimated model to make one-month-ahead forecasts. The out-of-sample performance of the proposed model is evaluated against a number of standard models. Various tests and accuracy measures are utilized to evaluate the forecast performances. It is found that forecasts from the nonnegative model perform exceptionally well under the mean absolute error and the mean absolute percentage error forecast accuracy measures.</p><p>In the fourth and last paper of the thesis we construct a multivariate extension of the popular Diebold-Mariano test. Under the null hypothesis of equal predictive accuracy of three or more forecasting models, the proposed test statistic has an asymptotic Chi-squared distribution. To explore whether the behavior of the test in moderate-sized samples can be improved, we also provide a finite-sample correction. A small-scale Monte Carlo study indicates that the proposed test has reasonable size properties in large samples and that it benefits noticeably from the finite-sample correction, even in quite large samples. The paper is concluded by an empirical example that illustrates the practical use of the two tests.</p>

This doctoral thesis is comprised of four papers that all relate to the subject of Time Series Analysis. The first paper of the thesis considers point estimation in a nonnegative, hence non-Gaussian, AR(1) model. The parameter estimation is carried out using a type of extreme value estimators (EVEs). A novel estimation method based on the EVEs is presented. The theoretical analysis is complemented with Monte Carlo simulation results and the paper is concluded by an empirical example. The second paper extends the model of the first paper of the thesis and considers semiparametric, robust point estimation in a nonlinear nonnegative autoregression. The nonnegative AR(1) model of the first paper is extended in three important ways: First, we allow the errors to be serially correlated. Second, we allow for heteroskedasticity of unknown form. Third, we allow for a multi-variable mapping of previous observations. Once more, the EVEs used for parameter estimation are shown to be strongly consistent under very general conditions. The theoretical analysis is complemented with extensive Monte Carlo simulation studies that illustrate the asymptotic theory and indicate reasonable small sample properties of the proposed estimators. In the third paper we construct a simple nonnegative time series model for realized volatility, use the results of the second paper to estimate the proposed model on S&amp;P 500 monthly realized volatilities, and then use the estimated model to make one-month-ahead forecasts. The out-of-sample performance of the proposed model is evaluated against a number of standard models. Various tests and accuracy measures are utilized to evaluate the forecast performances. It is found that forecasts from the nonnegative model perform exceptionally well under the mean absolute error and the mean absolute percentage error forecast accuracy measures. In the fourth and last paper of the thesis we construct a multivariate extension of the popular Diebold-Mariano test. Under the null hypothesis of equal predictive accuracy of three or more forecasting models, the proposed test statistic has an asymptotic Chi-squared distribution. To explore whether the behavior of the test in moderate-sized samples can be improved, we also provide a finite-sample correction. A small-scale Monte Carlo study indicates that the proposed test has reasonable size properties in large samples and that it benefits noticeably from the finite-sample correction, even in quite large samples. The paper is concluded by an empirical example that illustrates the practical use of the two tests.

Submitted by Eduardo Augusto Aun (auneduardo@gmail.com) on 2013-01-16T19:48:06Z No. of bitstreams: 1 DISSERTAÇÃO EDUARDO A AUN 2012 MPFE FGV.pdf: 1487732 bytes, checksum: 0fa68b5193a17357238c3ff083146e3d (MD5) / Approved for entry into archive by Eliene Soares da Silva (eliene.silva@fgv.br) on 2013-01-16T19:49:13Z (GMT) No. of bitstreams: 1 DISSERTAÇÃO EDUARDO A AUN 2012 MPFE FGV.pdf: 1487732 bytes, checksum: 0fa68b5193a17357238c3ff083146e3d (MD5) / Made available in DSpace on 2013-01-16T19:55:33Z (GMT). No. of bitstreams: 1 DISSERTAÇÃO EDUARDO A AUN 2012 MPFE FGV.pdf: 1487732 bytes, checksum: 0fa68b5193a17357238c3ff083146e3d (MD5) Previous issue date: 2012-12-18 / Este estudo compara previsões de volatilidade de sete ações negociadas na Bovespa usando 02 diferentes modelos de volatilidade realizada e 03 de volatilidade condicional. A intenção é encontrar evidências empíricas quanto à diferença de resultados que são alcançados quando se usa modelos de volatilidade realizada e de volatilidade condicional para prever a volatilidade de ações no Brasil. O período analisado vai de 01 de Novembro de 2007 a 30 de Março de 2011. A amostra inclui dados intradiários de 5 minutos. Os estimadores de volatilidade realizada que serão considerados neste estudo são o Bi-Power Variation (BPVar), desenvolvido por Barndorff-Nielsen e Shephard (2004b), e o Realized Outlyingness Weighted Variation (ROWVar), proposto por Boudt, Croux e Laurent (2008a). Ambos são estimadores não paramétricos, e são robustos a jumps. As previsões de volatilidade realizada foram feitas através de modelos autoregressivos estimados para cada ação sobre as séries de volatilidade estimadas. Os modelos de variância condicional considerados aqui serão o GARCH(1,1), o GJR (1,1), que tem assimetrias em sua construção, e o FIGARCH-CHUNG (1,d,1), que tem memória longa. A amostra foi divida em duas; uma para o período de estimação de 01 de Novembro de 2007 a 30 de Dezembro de 2010 (779 dias de negociação) e uma para o período de validação de 03 de Janeiro de 2011 a 31 de Março de 2011 (61 dias de negociação). As previsões fora da amostra foram feitas para 1 dia a frente, e os modelos foram reestimados a cada passo, incluindo uma variável a mais na amostra depois de cada previsão. As previsões serão comparadas através do teste Diebold-Mariano e através de regressões da variância ex-post contra uma constante e a previsão. Além disto, o estudo também apresentará algumas estatísticas descritivas sobre as séries de volatilidade estimadas e sobre os erros de previsão. / This study compares volatility forecasts of seven publicly traded companies using 2 different models of realized volatility and 3 models of conditional volatility. The intention is to find empirical evidence as to the difference in results that are achieved when using models of realized volatility and conditional volatility to predict the volatility of shares in Brazil. The sample period runs from 1 November 2007 to 30 March 2011. The sample includes 5 minutes intraday data. The realized volatility estimators that are considered in this study are the Bi-Power Variation (BPVar) developed by Barndorff-Nielsen and Shephard (2004b), and Weighted Realized Outlyingness Variation (ROWVar) proposed by Boudt, Croux and Laurent (2008a) . Both estimators are non-parametric, and are robust to jumps. The realized volatility forecasts were made by autoregressive models estimated for each share on the estimated volatility series. The conditional variance models considered here are the GARCH (1,1), the GJR (1,1), having asymmetries in its construction, and FIGARCH-CHUNG (1, d 1), having long memory. The sample was divided into two, one for the estimation period from 01 November 2007 to 30 December 2010 (779 trading days) and one for the validation period of 03 January 2011 to 31 March 2011 (61 trading days). The out of sample forecasts were made to 1 day ahead, and the models were reestimated at each step, including one more variable in the sample after each prediction. The predictions will be compared using the Diebold-Mariano test and through regressions of the variance ex-post against a constant and the prediction. Moreover, the study also shows some descriptive statistics on the estimated volatility series and on the forecasting errors.

Submitted by Sara Ribeiro (sara.ribeiro@ucb.br) on 2018-06-18T18:53:22Z No. of bitstreams: 1 RafaeldeMoraisVargasDissertacao2018.pdf: 2179808 bytes, checksum: e2993cd35f13b4bd6411d626aefa0043 (MD5) / Approved for entry into archive by Sara Ribeiro (sara.ribeiro@ucb.br) on 2018-06-18T18:54:14Z (GMT) No. of bitstreams: 1 RafaeldeMoraisVargasDissertacao2018.pdf: 2179808 bytes, checksum: e2993cd35f13b4bd6411d626aefa0043 (MD5) / Made available in DSpace on 2018-06-18T18:54:14Z (GMT). No. of bitstreams: 1 RafaeldeMoraisVargasDissertacao2018.pdf: 2179808 bytes, checksum: e2993cd35f13b4bd6411d626aefa0043 (MD5) Previous issue date: 2018-02-27 / Given the importance of market risk measures, such as value at risk (VaR), in this paper, we compare traditionally accepted volatility forecast models, in particular, the GARCH family models, with more recent models such as HAR-RV and GAS in terms of the accuracy of their VaR forecasts. For this purpose, we use intraday prices, at the 5-minute frequency, of the S&P 500 index and the General Electric stocks, for the period from January 4, 2010 to December 30, 2013. Based on the tick loss function and the Diebold-Mariano test, we did not find difference in the predictive performance of the HAR-RV and GAS models in comparison with the Exponential GARCH (EGARCH) model, considering daily VaR forecasts at the 1% and 5% significance levels for the return series of the S&P 500 index. Regarding the return series of General Electric, the 1% VaR forecasts obtained from the HAR-RV models, assuming a t-Student distribution for the daily returns, are more accurate than the forecasts of the EGARCH model. In the case of the 5% VaR forecasts, all variations of the HAR-RV model perform better than the EGARCH. Our empirical study provides evidence of the good performance of HAR-RV models in forecasting value at risk. / Dada a importância de medidas de risco de mercado, como o valor em risco (VaR), nesse trabalho, comparamos modelos de previsão de volatilidade tradicionalmente mais aceitos, em particular, os modelos da família GARCH, com modelos mais recentes, como o HAR-RV e o GAS, em termos da acurácia de suas previsões de VaR. Para isso, usamos preços intradiários, na frequência de 5 minutos, do índice S&P 500 e das ações da General Electric, para o período de 4 de janeiro de 2010 a 30 de dezembro de 2013. Com base na função perda tick e no teste de Diebold-Mariano, não encontramos diferença no desempenho preditivo dos modelos HAR-RV e GAS em relação ao modelo Exponential GARCH (EGARCH), considerando as previsões de VaR diário a 1% e 5% de significância para a série de retornos do índice S&P 500. Já com relação à série de retornos da General Electric, as previsões de VaR a 1% obtidas a partir dos modelos HAR-RV, assumindo uma distribuição t-Student para os retornos diários, mostram-se mais acuradas do que as previsões do modelo EGARCH. No caso das previsões de VaR a 5%, todas as variações do modelo HAR-RV apresentam desempenho superior ao EGARCH. Nosso estudo empírico traz evidências do bom desempenho dos modelos HAR-RV na previsão de valor em risco.

Submitted by Thiago Winkler Alves (thiagowinkler@gmail.com) on 2014-09-04T13:34:50Z No. of bitstreams: 1 forecasting-daily-volatility.pdf: 885976 bytes, checksum: 30fb655def03c3f3e61bf930b3a3585b (MD5) / Approved for entry into archive by JOANA MARTORINI (joana.martorini@fgv.br) on 2014-09-04T13:44:59Z (GMT) No. of bitstreams: 1 forecasting-daily-volatility.pdf: 885976 bytes, checksum: 30fb655def03c3f3e61bf930b3a3585b (MD5) / Made available in DSpace on 2014-09-04T13:51:17Z (GMT). No. of bitstreams: 1 forecasting-daily-volatility.pdf: 885976 bytes, checksum: 30fb655def03c3f3e61bf930b3a3585b (MD5) Previous issue date: 2014-08-06 / Aiming at empirical findings, this work focuses on applying the HEAVY model for daily volatility with financial data from the Brazilian market. Quite similar to GARCH, this model seeks to harness high frequency data in order to achieve its objectives. Four variations of it were then implemented and their fit compared to GARCH equivalents, using metrics present in the literature. Results suggest that, in such a market, HEAVY does seem to specify daily volatility better, but not necessarily produces better predictions for it, what is, normally, the ultimate goal. The dataset used in this work consists of intraday trades of U.S. Dollar and Ibovespa future contracts from BM&FBovespa. / Objetivando resultados empíricos, este trabalho tem foco na eaplicação do modelo HEAVY para volatilidade diária com dados financeiros do mercado Brasileiro. Muito similar ao GARCH, este modelo busca explorar dados em alta frequência para atingir seus objetivos. Quatro variações dele foram então implementadas e seus ajustes comparadados a equivalentes GARCH, utilizando métricas presentes na literatura. Os resultados sugerem que, neste mercado, o HEAVY realmente parece especificar melhor a volatilidade diária, mas não necessariamente produz melhores previsões, o que, normalmente, é o objetivo final. A base de dados utilizada neste trabalho consite de negociações intradiárias de contratos futuros de dólares americanos e Ibovespa da BM&FBovespa.