Duration models are often concerned with time intervals between trades, longer durations indicating a lack of trading activities. In this thesis, we study parameter estimation for the Autoregressive Conditional Duration (ACD) and Stochastic Conditional Duration (SCD) models. Maximum likelihood methods can usually be used in the case of ACD models. However, the SCD models are based on the assumption that durations are generated by a dynamic stochastic latent variable which is often perturbed by Exponential, Weibull, Gamma or Log-Normal distributed innovations. This makes the use of maximum likelihood methods difficult. One alternative method of parameter estimation, in this case, consists in using quasi-maximum likelihood after transforming the original nonlinear model into a state-space model and using the Kalman filter, a similar filtering scheme or the Generalized Method of Moments (GMM). We use the nonlinear filter and GMM method to analyze the Quadratic Stochastic Conditional duration model as well.

Duration models are often concerned with time intervals between trades, longer durations indicating a lack of trading activities. In this thesis, we study parameter estimation for the Autoregressive Conditional Duration (ACD) and Stochastic Conditional Duration (SCD) models. Maximum likelihood methods can usually be used in the case of ACD models. However, the SCD models are based on the assumption that durations are generated by a dynamic stochastic latent variable which is often perturbed by Exponential, Weibull, Gamma or Log-Normal distributed innovations. This makes the use of maximum likelihood methods difficult. One alternative method of parameter estimation, in this case, consists in using quasi-maximum likelihood after transforming the original nonlinear model into a state-space model and using the Kalman filter, a similar filtering scheme or the Generalized Method of Moments (GMM). We use the nonlinear filter and GMM method to analyze the Quadratic Stochastic Conditional duration model as well.

<p>In this thesis, we apply the Ordinary Least Squares (OLS) and the Generalized Least Squares (GLS) methods for the estimation of Autoregressive Conditional Duration (ACD) models, as opposed to the typical approach of using the Quasi Maximum Likelihood Estimation (QMLE).</p> <p>The advantages of OLS and GLS as the underlying methods of estimation lie in their theoretical ease and computational convenience. The latter property is crucial for high frequency trading, where a transaction decision needs to be made within a minute. We show that both OLS and GLS estimates are asymptotically consistent and normally distributed. The normal approximation does not seem to be satisfactory in small samples. We also apply Residual Bootstrap to construct the confidence intervals based on the OLS and GLS estimates. The properties of the proposed methods are illustrated with intensive numerical simulations as well as by a case study on the IBM transaction data.</p> / Master of Science (MSc)

Submitted by Carlos Barros (cfbarros@americastg.com) on 2015-09-01T13:02:06Z No. of bitstreams: 1 Dissertação - Carlos Felipe Barros.docx: 511698 bytes, checksum: 15dad3f7330f64c20af5761c41ea0ef2 (MD5) / Approved for entry into archive by GILSON ROCHA MIRANDA (gilson.miranda@fgv.br) on 2015-09-01T15:48:20Z (GMT) No. of bitstreams: 1 Dissertação - Carlos Felipe Barros.docx: 511698 bytes, checksum: 15dad3f7330f64c20af5761c41ea0ef2 (MD5) / Approved for entry into archive by Marcia Bacha (marcia.bacha@fgv.br) on 2015-09-02T13:37:45Z (GMT) No. of bitstreams: 1 Dissertação - Carlos Felipe Barros.docx: 511698 bytes, checksum: 15dad3f7330f64c20af5761c41ea0ef2 (MD5) / Made available in DSpace on 2015-09-02T13:37:58Z (GMT). No. of bitstreams: 1 Dissertação - Carlos Felipe Barros.docx: 511698 bytes, checksum: 15dad3f7330f64c20af5761c41ea0ef2 (MD5) Previous issue date: 2013-05-29 / The objective of this paper is to estimate a dynamic market depth measure, called VNET, for Brazilian stocks using transactions data. VNET gauges the difference between the numbers of buyer- and seller-initiated trades within the time it takes for the stock price to change by at least a certain amount. It is a realized measure of liquidity for a given price deterioration, which one may track throughout the trading day to capture liquidity’s short-term dynamics. More specifically, we model the price duration using an autoregressive conditional duration (ACD) model. The predetermined nature of the ACD process is convenient because it makes it possible to forecast future changes in the liquidity of a stock. By identifying the best moment to buy or sell, the VNET is an excellent starting point for any optimal execution strategy. Our empirical findings indicate that the VNET measure of market depth depends on the bid-ask spread, volume traded, number of trades, and both expected and unexpected price durations. Finally, we also estimate the price impact of a trade by varying the increment in the definition of price duration. / O objetivo desse trabalho é encontrar uma medida dinâmica de liquidez de ações brasileiras, chamada VNET. Foram utilizados dados de alta frequência para criar um modelo capaz de medir o excesso de compras e vendas associadas a um movimento de preços. Ao variar no tempo, o VNET pode ser entendido como a variação da proporção de agentes informados em um modelo de informação assimétrica. Uma vez estimado, ele pode ser utilizado para prever mudanças na liquidez de uma ação. O VNET tem implicações práticas importantes, podendo ser utilizado por operadores como uma medida estocástica para identificar quais seriam os melhores momentos para operar. Gerentes de risco também podem estimar a deterioração de preço esperada ao se liquidar uma posição, sendo possível analisar suas diversas opções, servindo de base para otimização da execução. Na construção do trabalho encontramos as durações de preço de cada ação e as diversas medidas associadas a elas. Com base nos dados observa-se que a profundidade varia com ágio de compra e venda, com o volume negociado, com o numero de negócios, com a duração de preços condicional e com o seu erro de previsão. Os resíduos da regressão de VNET se mostraram bem comportados o que corrobora a hipótese de que o modelo foi bem especificado. Para estimar a curva de reação do mercado, variamos os intervalos de preço usados na definição das durações.