This thesis examines an impact of high frequency trading on equity market qualities. As an indicator of market quality, stock prices realized volatility is used. To estimate the high frequency trading activity, we implement a special method of identification of high frequency orders from quote data. Study of relation between high frequency trading and market qualities is incited by growing concerns about the welfare impacts of high frequency trading and connected activities. In order to test the dependence and causality between high frequency trading activity and volatility, we implement time-scale estimation techniques. Wavelet coherence is used to study localized dependence. The analysis is amended by a robustness check, using wavelet correlation. Results show inconsistent dependence at short trading horizons and regions of significant continuous dependence at trading horizons within hours. Powered by TCPDF (www.tcpdf.org)

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&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.

Neste trabalho, visamos mostrar as características usuais dos dados de alta frequência, bem como utilizar modelagem não paramétrica para estimar a variância/volatilidade para esses dados. Após uma revisão sobre microestrutura de mercado, sazonalidade intradiária, variação quadrática e saltos, utilizamos os dados da PETR4 para estimar a variância realizada e variação bipotente. Determinadas essas séries, testamos se há saltos nas mesmas. Em seguida, analisamos o impacto que a microestrutura de mercado e a sazonalidade intradiária causam na detecção dos saltos. Concluímos que, enquanto a presença de microestrutura aponta para um número de saltos menor que o esperado, a sazonalidade intradiária aponta para o lado contrário, ou seja, ela causa um viés para detectar mais saltos, dada a estrutura típica da curva de volatilidade ao longo do dia em formato de J invertido, causando mais saltos incorretamente detectados no período mais volátil do dia (que corresponde a abertura da bolsa de valores). / In this work, we aim to show the usual characteristics of high-frequency data and the estimation of variance/volatility for this kind of data using nonparametric models. After reviewing concepts about market microstructure, intraday seasonality, quadratic variation and jumps, we use PETR4 data to estimate realized variance and bipower variation. With these series determined, we test for jumps. Then, we analyze the impact that market microstructure and intraday seasonality causes in jump detection. We conclude that while microstructure noise indicates fewer jumps than the ideal amount, intraday seasonality goes in the opposite direction, i.e., it detects more jumps than it should, since the typical inverted-J-shaped intraday volatility pattern tends to incorrectly detect more jumps at the most volatile period (which is when stock markets start negotiations).

Neste trabalho, visamos mostrar as características usuais dos dados de alta frequência, bem como utilizar modelagem não paramétrica para estimar a variância/volatilidade para esses dados. Após uma revisão sobre microestrutura de mercado, sazonalidade intradiária, variação quadrática e saltos, utilizamos os dados da PETR4 para estimar a variância realizada e variação bipotente. Determinadas essas séries, testamos se há saltos nas mesmas. Em seguida, analisamos o impacto que a microestrutura de mercado e a sazonalidade intradiária causam na detecção dos saltos. Concluímos que, enquanto a presença de microestrutura aponta para um número de saltos menor que o esperado, a sazonalidade intradiária aponta para o lado contrário, ou seja, ela causa um viés para detectar mais saltos, dada a estrutura típica da curva de volatilidade ao longo do dia em formato de J invertido, causando mais saltos incorretamente detectados no período mais volátil do dia (que corresponde a abertura da bolsa de valores). / In this work, we aim to show the usual characteristics of high-frequency data and the estimation of variance/volatility for this kind of data using nonparametric models. After reviewing concepts about market microstructure, intraday seasonality, quadratic variation and jumps, we use PETR4 data to estimate realized variance and bipower variation. With these series determined, we test for jumps. Then, we analyze the impact that market microstructure and intraday seasonality causes in jump detection. We conclude that while microstructure noise indicates fewer jumps than the ideal amount, intraday seasonality goes in the opposite direction, i.e., it detects more jumps than it should, since the typical inverted-J-shaped intraday volatility pattern tends to incorrectly detect more jumps at the most volatile period (which is when stock markets start negotiations).

Neste trabalho, visamos mostrar as características usuais dos dados de alta frequência, bem como utilizar modelagem não paramétrica para estimar a variância/volatilidade para esses dados. Após uma revisão sobre microestrutura de mercado, sazonalidade intradiária, variação quadrática e saltos, utilizamos os dados da PETR4 para estimar a variância realizada e variação bipotente. Determinadas essas séries, testamos se há saltos nas mesmas. Em seguida, analisamos o impacto que a microestrutura de mercado e a sazonalidade intradiária causam na detecção dos saltos. Concluímos que, enquanto a presença de microestrutura aponta para um número de saltos menor que o esperado, a sazonalidade intradiária aponta para o lado contrário, ou seja, ela causa um viés para detectar mais saltos, dada a estrutura típica da curva de volatilidade ao longo do dia em formato de J invertido, causando mais saltos incorretamente detectados no período mais volátil do dia (que corresponde a abertura da bolsa de valores). / In this work, we aim to show the usual characteristics of high-frequency data and the estimation of variance/volatility for this kind of data using nonparametric models. After reviewing concepts about market microstructure, intraday seasonality, quadratic variation and jumps, we use PETR4 data to estimate realized variance and bipower variation. With these series determined, we test for jumps. Then, we analyze the impact that market microstructure and intraday seasonality causes in jump detection. We conclude that while microstructure noise indicates fewer jumps than the ideal amount, intraday seasonality goes in the opposite direction, i.e., it detects more jumps than it should, since the typical inverted-J-shaped intraday volatility pattern tends to incorrectly detect more jumps at the most volatile period (which is when stock markets start negotiations).

本文以日內資料研究台灣證券交易所於2005年3月1日實施股價升降單位新制後，市場交易因子與股價報酬波動率的變化；延伸討論市場參與者對新訊息之反應，進而評估實施股價升降單位新制之成效。本文首先比較四種常用來衡量報酬波動率的方法，並從中挑選出最穩健的測度方式；接著藉此分析股價日報酬波動率與市場交易因子之間的關係；最後，由於日內股價報酬波動的軌跡呈現U型曲線，為突顯波動較劇烈之時段股價報酬波動率是否亦隨股價升降單位縮小而趨緩，故著眼交易日開盤後一小時及收盤前一小時，再次檢驗上述關係。實證結果支持股價升降單位縮小使實現波動率大幅降低且交易筆數密切影響股價報酬波動率，且不論在日資料與日內資料都呈現相似結論；並發現愈接近開、收盤的時間點，股價報酬波動率降低比例亦愈大，顯示升降單位新制達成政策目的。 / In this study, we address the impact of the tick size reduction on the Taiwan Stock Exchange on March 1, 2005. We propose to investigate the variations of trading activities and return volatility, discuss investors' behaviors to the new information and evaluate the tick size reduction by analyzing intraday data. First, we select the most robust volatility measure for our study from four commonly used ones. Second, we examine the relationship between daily return volatility and trading activities. Eventually, due to the commonly observed U-shaped pattern of intraday return volatility, we re-examine the intraday relation between return volatility and trading activities. Our empirical results based on the robust realized volatility confirm that both daily and intraday return volatility decline significantly after the tick size reduction, and number of trades is a prominent trading factor in explaining realized volatility. More interestingly, we observe that the percentage decrease in realized volatility is most pronounced for trading sessions near the beginning or the ending of each trading day. Overall, our empirical findings support the arguments for tick size reduction intended by policymakers.

Le prix efficient est latent, il est contaminé par les frictions microstructurelles ou bruit. On explore la mesure et la prévision de la volatilité fondamentale en utilisant les données à haute fréquence. Dans le premier papier, en maintenant le cadre standard du modèle additif du bruit et le prix efficient, on montre qu’en utilisant le volume de transaction, les volumes d’achat et de vente, l’indicateur de la direction de transaction et la différence entre prix d’achat et prix de vente pour absorber le bruit, on améliore la précision des estimateurs de volatilité. Si le bruit n’est que partiellement absorbé, le bruit résiduel est plus proche d’un bruit blanc que le bruit original, ce qui diminue la misspécification des caractéristiques du bruit. Dans le deuxième papier, on part d’un fait empirique qu’on modélise par une forme linéaire de la variance du bruit microstructure en la volatilité fondamentale. Grâce à la représentation de la classe générale des modèles de volatilité stochastique, on explore la performance de prévision de différentes mesures de volatilité sous les hypothèses de notre modèle. Dans le troisième papier, on dérive de nouvelles mesures réalizées en utilisant les prix et les volumes d’achat et de vente. Comme alternative au modèle additif standard pour les prix contaminés avec le bruit microstructure, on fait des hypothèses sur la distribution du prix sans frictions qui est supposé borné par les prix de vente et d’achat. / The high frequency observed price series is contaminated with market microstructure frictions or noise. We explore the measurement and forecasting of the fundamental volatility through novel approaches to the frictions’ problem. In the first paper, while maintaining the standard framework of a noise-frictionless price additive model, we use the trading volume, quoted depths, trade direction indicator and bid-ask spread to get rid of the noise. The econometric model is a price impact linear regression. We show that incorporating the cited liquidity costs variables delivers more precise volatility estimators. If the noise is only partially absorbed, the remaining noise is closer to a white noise than the original one, which lessens misspecification of the noise characteristics. Our approach is also robust to a specific form of endogeneity under which the common robust to noise measures are inconsistent. In the second paper, we model the variance of the market microstructure noise that contaminates the frictionless price as an affine function of the fundamental volatility. Under our model, the noise is time-varying intradaily. Using the eigenfunction representation of the general stochastic volatility class of models, we quantify the forecasting performance of several volatility measures under our model assumptions. In the third paper, instead of assuming the standard additive model for the observed price series, we specify the conditional distribution of the frictionless price given the available information which includes quotes and volumes. We come up with new volatility measures by characterizing the conditional mean of the integrated variance.

In this work, neural networks are used to forecast daily Realized Volatility of the EUR/USD, GBP/USD and USD/CHF currency pairs time series. Their performan-ce is benchmarked against nowadays popular Hetero-genous Autoregressive model of Realized Volatility (HAR) and traditional ARIMA models. As a by-product of our research, we introduce a simple yet effective enhancement to HAR model, naming the new model HARD extension. Forecasting performance tests of HARD model are conducted as well, promoting it to become a reference benchmark for neural networks and ARIMA.

Operações em alta frequência demonstraram crescimento nos últimos anos; em decorrência disso, surgiu a necessidade de estudar o mercado de ações brasileiro no contexto dos dados em alta frequência. Os estimadores da volatilidade dos preços de ações utilizando dados de negociações em alta frequência são os principais objetos de estudo. Conforme Aldridge (2010) e Vuorenmaa (2013), o HFT foi definido como a rápida realocação de capital feita de modo que as transações possam ocorrer em milésimos de segundos por uso de algoritmos complexos que gerenciam envio de ordens, análise dos dados obtidos e tomada das melhores decisões de compra e venda. A principal fonte de informações para análise do HFT são os dados tick by tick, conhecidos como dados em alta frequência. Uma métrica oriunda da análise de dados em alta frequência e utilizada para gestão de riscos é a Volatilidade Percebida. Conforme Andersen et al. (2003), Pong et al. (2004), Koopman et al. (2005) e Corsi (2009) há um consenso na área de finanças de que as projeções da volatilidade utilizando essa métrica de risco são mais eficientes de que a estimativa da volatilidade por meio de modelos GARCH. Na gestão financeira, a projeção da volatilidade é uma ferramenta fundamental para provisionar reservas para possíveis perdas;, devido à existência de vários métodos de projeção da volatilidade e em decorrência desta necessidade torna-se necessário selecionar um modelo ou combinar diversas projeções. O principal desafio para combinar projeções é a escolha dos pesos: as diversas pesquisas da área têm foco no desenvolvimento de métodos para escolhê-los visando minimizar os erros de previsão. A literatura existente carece, no entanto, de uma proposição de método que considere o problema de eventual projeção de volatilidade abaixo do esperado. Buscando preencher essa lacuna, o objetivo principal desta tese é propor uma combinação dos estimadores da volatilidade dos preços de ações utilizando dados de negociações em alta frequência para o mercado brasileiro. Como principal ponto de inovação, propõe-se aqui de forma inédita a utilização da função baseada no Lower Partial Moment (LPM) para estimativa dos pesos para combinação das projeções. Ainda que a métrica LPM seja bastante conhecida na literatura, sua utilização para combinação de projeções ainda não foi analisada. Este trabalho apresenta contribuições ao estudo de combinações de projeções realizadas pelos modelos HAR, MIDAS, ARFIMA e Nearest Neighbor, além de propor dois novos métodos de combinação -- estes denominados por LPMFE (Lower Partial Moment Forecast Error) e DLPMFE (Discounted LPMFE). Os métodos demonstraram resultados promissores pretendem casos cuja pretensão seja evitar perdas acima do esperado e evitar provisionamento excessivo do ponto de vista orçamentário. / The High Frequency Trading (HFT) has grown significantly in the last years, in this way, this raises the need for research of the high frequency data on the Brazilian stock market.The volatility estimators of the asset prices using high frequency data are the main objects of study. According to Aldridge (2010) and Vuorenmaa (2013), the HFT was defined as the fast reallocation of trading capital that the negotiations may occur on milliseconds by complex algorithms scheduled for optimize the process of sending orders, data analysis and to make the best decisions of buy or sell. The principal information source for HFT analysis is the tick by tick data, called as high frequency data. The Realized Volatility is a risk measure from the high frequency data analysis, this metric is used for risk management.According to Andersen et al. (2003), Pong et al. (2004), Koopman et al.(2005) and Corsi (2009) there is a consensus in the finance field that the volatility forecast using this risk measure produce better results than estimating the volatility by GARCH models. The volatility forecasting is a key issue in the financial management to provision capital resources to possible losses. However, because there are several volatility forecast methods, this problem raises the need to choice a specific model or combines the projections. The main challenge to combine forecasts is the choice of the weights, with the aim of minimizingthe forecast errors, several research in the field have been focusing on development of methods to choice the weights.Nevertheless, it is missing in the literature the proposition of amethod which consider the minimization of the risk of an inefficient forecast for the losses protection. Aiming to fill the gap, the main goal of the thesis is to propose a combination of the asset prices volatility forecasts using high frequency data for Brazilian stock market. As the main focus of innovation, the thesis proposes, in an unprecedented way, the use of the function based on the Lower Partial Moment (LPM) to estimate the weights for the combination of volatility forecasts. Although the LPM measure is well known in the literature, the use of this metric for forecast combination has not been yet studied.The thesis contributes to the literature when studying the forecasts combination made by the models HAR, MIDAS, ARFIMA and Nearest Neighbor. The thesis also contributes when proposing two new methods of combinations, these methodologies are referred to as LPMFE (Lower Partial Moment Forecast Error) and DLPMFE (Discounted LPMFE). The methods have shown promising results when it is intended to avoid losses above the expected it is not intended to cause provisioning excess in the budget.

This thesis uses Heterogeneous Autoregressive models of Realized Volatility on five-minute data of three of the most liquid financial assets - S&P 500 Futures index, Euro FX and Light Crude NYMEX. The main contribution lies in the length of the datasets which span the time period of 25 years (13 years in case of Euro FX). Our aim is to show that decomposing realized variance into continuous and jump components improves the predicatability of RV also on extremely long high frequency datasets. The main goal is to investigate the dynamics of the HAR model parameters in time. Also, we examine if volatilities of various assets behave differently. The results reveal that decomposing RV into its components indeed im- proves the modeling and forecasting of volatility on all datasets. However, we found that forecasts are best when based on short, 1-2 years, pre-forecast periods due to high dynamics of HAR model's parameters in time. This dynamics is revealed also by a year-by-year estimation on all datasets. Con- sequently, we consider HAR models to be inapproppriate for modeling RV on such long datasets as they are not able to capture the dynamics of RV. This was indicated on all three datasets, thus, we conclude that volatility behaves similarly for different types of assets with similar liquidity. 1