A family of autoregressive conditional duration models

This paper develops a family of autoregressive conditional duration (ACD) models that encompasses most specifications in the literature. The nesting relies on a Box-Cox transformation with shape parameter λ to the conditional duration process and a possibly asymmetric shocks impact curve. We establish conditions for the existence of higher-order moments, strict stationarity, geometric ergodicity and β-mixing property with exponential decay. We next derive moment recursion relations and the autocovariance function of the power λ of the duration process. Finally, we assess the practical usefulness of our family of ACD models using NYSE transactions data, with special attention to IBM price durations. The results warrant the extra flexibility provided either by the Box-Cox transformation or by the asymmetric response to shocks.

A family of autoregressive conditional duration models

This paper develops a family of autoregressive conditional duration (ACD) models that encompasses most specifications in the literature. The nesting relies on a Box-Cox transformation with shape parameter λ to the conditional duration process and a possibly asymmetric shocks impact curve. We establish conditions for the existence of higher-order moments, strict stationarity, geometric ergodicity and β-mixing property with exponential decay. We next derive moment recursion relations and the autocovariance function of the power λ of the duration process. Finally, we assess the practical usefulness of our family of ACD models using NYSE price duration data on the IBM stock. The results warrant the extra flexibility provided either by the Box-Cox transformation or by the asymmetric response to shocks.

Testing the Markov property with ultra high frequency financial data

This paper develops a framework to test whether discrete-valued irregularly-spaced financial transactions data follow a subordinated Markov process. For that purpose, we consider a specific optional sampling in which a continuous-time Markov process is observed only when it crosses some discrete level. This framework is convenient for it accommodates not only the irregular spacing of transactions data, but also price discreteness. Further, it turns out that, under such an observation rule, the current price duration is independent of previous price durations given the current price realization. A simple nonparametric test then follows by examining whether this conditional independence property holds. Finally, we investigate whether or not bid-ask spreads follow Markov processes using transactions data from the New York Stock Exchange. The motivation lies on the fact that asymmetric information models of market microstructures predict that the Markov property does not hold for the bid-ask spread. The results are mixed in the sense that the Markov assumption is rejected for three out of the five stocks we have analyzed.

Profundidade de mercado na BM&FBovespa: um modelo de alta frequência para estimação da profundidade de mercado da BM&FBovespa

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.

A (semi-)parametric functional coefficient autoregressive conditional duration model

In this paper, we propose a class of ACD-type models that accommodates overdispersion, intermittent dynamics, multiple regimes, and sign and size asymmetries in financial durations. In particular, our functional coefficient autoregressive conditional duration (FC-ACD) model relies on a smooth-transition autoregressive specification. The motivation lies on the fact that the latter yields a universal approximation if one lets the number of regimes grows without bound. After establishing that the sufficient conditions for strict stationarity do not exclude explosive regimes, we address model identifiability as well as the existence, consistency, and asymptotic normality of the quasi-maximum likelihood (QML) estimator for the FC-ACD model with a fixed number of regimes. In addition, we also discuss how to consistently estimate using a sieve approach a semiparametric variant of the FC-ACD model that takes the number of regimes to infinity. An empirical illustration indicates that our functional coefficient model is flexible enough to model IBM price durations.

Non- parametric specification tests for conditional duration models

This paper deals with the estimation and testing of conditional duration models by looking at the density and baseline hazard rate functions. More precisely, we foeus on the distance between the parametric density (or hazard rate) function implied by the duration process and its non-parametric estimate. Asymptotic justification is derived using the functional delta method for fixed and gamma kernels, whereas finite sample properties are investigated through Monte Carlo simulations. Finally, we show the practical usefulness of such testing procedures by carrying out an empirical assessment of whether autoregressive conditional duration models are appropriate to oIs for modelling price durations of stocks traded at the New York Stock Exchange.

Are price limits on futures markets that cool? evidence from the brazilian merchantile & futures exchange

This paper investigates the impact of price limits on the Brazil- ian future markets using high frequency data. The aim is to identify whether there is a cool-off or a magnet effect. For that purpose, we examine a tick-by-tick data set that includes all contracts on the São Paulo stock index futures traded on the Brazilian Mercantile and Futures Exchange from January 1997 to December 1999. Our main finding is that price limits drive back prices as they approach the lower limit. There is a strong cool-off effect of the lower limit on the conditional mean, whereas the upper limit seems to entail a weak magnet effect on the conditional variance. We then build a trading strategy that accounts for the cool-off effect so as to demonstrate that the latter has not only statistical, but also economic signifi- cance. The resulting Sharpe ratio indeed is way superior to the buy-and-hold benchmarks we consider.

Nonparametric specification tests for conditional duration models

This paper deals with the testing of autoregressive conditional duration (ACD) models by gauging the distance between the parametric density and hazard rate functions implied by the duration process and their non-parametric estimates. We derive the asymptotic justification using the functional delta method for fixed and gamma kernels, and then investigate the finite-sample properties through Monte Carlo simulations. Although our tests display some size distortion, bootstrapping suffices to correct the size without compromising their excellent power. We show the practical usefulness of such testing procedures for the estimation of intraday volatility patterns.

First-Price auction symmetric equlibria with a general distribution

In this paper I obtain the mixed strategy symmetric equilibria of the first-price auction for any distribution. The equilibrium is unique. The solution turns out to be a combination of absolutely continuous distributions case and the discrete distributions case.

Is there a price puzzle in Brazil? An application of Bias-Corrected Bootstrap

Using data from the United States, Japan, Germany , United Kingdom and France, Sims (1992) found that positive innovations to shortterm interest rates led to sharp, persistent increases in the price level. The result was conÖrmed by other authors and, as a consequence of its non-expectable nature, was given the name "price puzzle" by Eichenbaum (1992). In this paper I investigate the existence of a price puzzle in Brazil using the same type of estimation and benchmark identiÖcation scheme employed by Christiano et al. (2000). In a methodological improvement over these studies, I qualify the results with the construction of bias-corrected bootstrap conÖdence intervals. Even though the data does show the existence of a statistically signiÖcant price puzzle in Brazil, it lasts for only one quarter and is quantitatively immaterial

First-price auction symmetric equilibria with a general distribution

In this paper I obtain the mixed strategy symmetric equilibria of the first-price auction for any distribution. The equilibrium is unique. The solution turns out to be a combination of absolutely continuous distributions case and the discrete distributions case.

Purchasing power parity: the choice of price index

Looking closely at the PPP argument, it states that the currencies purchasing power should not change when comparing the same basket goods across countries, and these goods should all be tradable. Hence, if PPP is valid at all, it should be captured by the relative price indices that best Öts these two features. We ran a horse race among six di§erent price indices available from the IMF database to see which one would yield higher PPP evidence, and, therefore, better Öt the two features. We used RER proxies measured as the ratio of export unit values, wholesale prices, value added deáators, unit labor costs, normalized unit labor costs and consumer prices, for a sample of 16 industrial countries, with quarterly data from 1975 to 2002. PPP was tested using both the ADF and the DFGLS unit root test of the RER series. The RER measured as WPI ratios was the one for which PPP evidence was found for the larger number of countries: six out of sixteen when we use DF-GLS test with demeaned series. The worst measure of all was the RER based on the ratio of foreign CPIs and domestic WPI. No evidence of PPP at all was found for this measure.

Are price limits on futures markets that cool?: evidence from the Brazilian Mercantile and Futures Exchange

This paper investigates the impact of price limits on the Brazilian futures markets using high frequency data. The aim is to identify whether there is a cool-off or a magnet effect. For that purpose, we examine a tick-by-tick data set that includes all contracts on the S˜ao Paulo stock index futures traded on the Brazilian Mercantile and Futures Exchange from January 1997 to December 1999. The results indicate that the conditional mean features a floor cool-off effect, whereas the conditional variance significantly increases as the price approaches the upper limit. We then build a trading strategy that accounts for the cool-off effect in the conditional mean so as to demonstrate that the latter has not only statistical, but also economic significance. The in-sample Sharpe ratio indeed is way superior to the buy-and-hold benchmarks we consider, whereas out-of-sample results evince similar performances.