Testing unit root based on partially adaptive estimation

This paper proposes unit tests based on partially adaptive estimation. The proposed tests provide an intermediate class of inference procedures that are more efficient than the traditional OLS-based methods and simpler than unit root tests based on fully adptive estimation using nonparametric methods. The limiting distribution of the proposed test is a combination of standard normal and the traditional Dickey-Fuller (DF) distribution, including the traditional ADF test as a special case when using Gaussian density. Taking into a account the well documented characteristic of heavy-tail behavior in economic and financial data, we consider unit root tests coupled with a class of partially adaptive M-estimators based on the student-t distributions, wich includes te normal distribution as a limiting case. Monte Carlo Experiments indicate that, in the presence of heavy tail distributions or innovations that are contaminated by outliers, the proposed test is more powerful than the traditional ADF test. We apply the proposed test to several macroeconomic time series that have heavy-tailed distributions. The unit root hypothesis is rejected in U.S. real GNP, supporting the literature of transitory shocks in output. However, evidence against unit roots is not found in real exchange rate and nominal interest rate even haevy-tail is taken into a account.

The Brazilian credit market for small and medium-sized firms: an adaptive marketing approach

Neste trabalho, o mercado brasileiro de crédito para pequenas e médias empresas (PMEs) é analisado sob a perspectiva do marketing adaptativo, em que se assume que atividades mercadológicas como segmentação, gestão de relacionamento com clientes, apreçamento e desenvolvimento de produtos, são determinadas pela utilidade obtida por agentes de mercado ao atenderem a demanda. Identifica-se que a existência de assimetria de informações e de custos de transação limita e direciona as atividades de marketing no mercado estudado. A partir de uma amostra com 65.535 propostas de crédito, recebidas e avaliadas por um grande banco brasileiro entre janeiro de 2004 e setembro de 2006, estima-se a utilidade do banco em operações de crédito. Adicionalmente, 17.149 transações de empréstimos concedidos pelo banco ao segmento de pequenas empresas entre abril de 2006 e março de 2007, são investigadas. Finalmente, um conjunto de dados com 1,636 registros obtidos pela junção das bases de dados de propostas e de transações mencionados, é analisado em termos das relações entre taxas de juros e os totais de cobertura oferecidas por meio de garantias de crédito. Os resultados revelam a existência de um ambiente de marketing adaptativo, em que os pequenos tomadores de crédito produtivo são racionados, e aceitam pagar taxas de juros mais elevadas do que outros segmentos. Produtos de créditos baseados em garantias líquidas e com altas taxas de juros são desenvolvidos para suprir de maneira oportuna este segmento racionado de pequenas empresas. Ademais, a utilidade do banco em operações de crédito é afetada pela informação privada que captura ao longo de relacionamentos mantidos com seus cientes. Os resultados implicam que o sistema de marketing financeiro brasileiro não desempenha papel formativo no desenvolvimento econômico, que seria de fomento ao crédito produtivo por meio de empréstimos a baixo custo para pequenas e médias empresas. Um sistema formativo de marketing é improvável em um ambiente com informação imperfeita, como o mercado de crédito brasileiro. O estudo traz informações úteis àqueles interessados no desenvolvimento de mercados de crédito produtivo, tais como profissionais de instituições financeiras; agentes responsáveis por políticas públicas e monetárias de fomento ao crédito; e empreendedores de pequeno e médio porte que necessitem de financiamento externo para seus negócios.

Convex combinations of long memory estimates from different sampling rates

Convex combinations of long memory estimates using the same data observed at different sampling rates can decrease the standard deviation of the estimates, at the cost of inducing a slight bias. The convex combination of such estimates requires a preliminary correction for the bias observed at lower sampling rates, reported by Souza and Smith (2002). Through Monte Carlo simulations, we investigate the bias and the standard deviation of the combined estimates, as well as the root mean squared error (RMSE), which takes both into account. While comparing the results of standard methods and their combined versions, the latter achieve lower RMSE, for the two semi-parametric estimators under study (by about 30% on average for ARFIMA(0,d,0) series).

A unit root test based on partially adaptive estimation

This paper constructs a unit root test baseei on partially adaptive estimation, which is shown to be robust against non-Gaussian innovations. We show that the limiting distribution of the t-statistic is a convex combination of standard normal and DF distribution. Convergence to the DF distribution is obtaineel when the innovations are Gaussian, implying that the traditional ADF test is a special case of the proposed testo Monte Carlo Experiments indicate that, if innovation has heavy tail distribution or are contaminated by outliers, then the proposed test is more powerful than the traditional ADF testo Nominal interest rates (different maturities) are shown to be stationary according to the robust test but not stationary according to the nonrobust ADF testo This result seems to suggest that the failure of rejecting the null of unit root in nominal interest rate may be due to the use of estimation and hypothesis testing procedures that do not consider the absence of Gaussianity in the data.Our results validate practical restrictions on the behavior of the nominal interest rate imposed by CCAPM, optimal monetary policy and option pricing models.

Convergence analysis of sampling-based decomposition methods for risk-averse multistage stochastic convex programs

We consider a class of sampling-based decomposition methods to solve risk-averse multistage stochastic convex programs. We prove a formula for the computation of the cuts necessary to build the outer linearizations of the recourse functions. This formula can be used to obtain an efficient implementation of Stochastic Dual Dynamic Programming applied to convex nonlinear problems. We prove the almost sure convergence of these decomposition methods when the relatively complete recourse assumption holds. We also prove the almost sure convergence of these algorithms when applied to risk-averse multistage stochastic linear programs that do not satisfy the relatively complete recourse assumption. The analysis is first done assuming the underlying stochastic process is interstage independent and discrete, with a finite set of possible realizations at each stage. We then indicate two ways of extending the methods and convergence analysis to the case when the process is interstage dependent.