CEMAPRE - Documentos de Trabalho / CEMAPRE - Working Papers
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- A tree combinatorial structure on the solution of a delay differential equation: a generating function approachPublication . Fabião, Maria de Fátima; Brito, Paulo; St. Aubyn, AntónioThis paper introduces a new approach for obtaining explicit solutions for a first order linear delay differential equation with constant coefficients. We conjecture that there is a generating function defined over of a specific class of polynomials in the delay that solves the equation, and prove in the main theorem that the conjecture is valid. We also show the advantage of our method as regards the traditional Method of Step Algorithm (MSA).
- Covariate measurement error : bias reduction under response-based samplingPublication . Ramalho, Esmeralda A.In this paper we propose a general framework to deal with the presence of covariate measurement error (CME) in response-based (RB) samples. Using Chesher’s (1991) methodology, we obtain a small error variance approximation for the contaminated sampling distributions that characterise RB samples with CME. Then, following Chesher (2000), we develop generalised method of moments (GMM) estimators that reduce the bias of the most well known likelihood-based estimators for RB samples which ignore the existence of CME and derive a score test to detect the presence of this type of measurement error. Our approach only requires the specification of the conditional distribution of the response variable given the latent covariates and the classical additive measurement error model assumption, the availability of information on both the marginal probability of the strata in the population and the variance of the measurement error not being essential. Monte Carlo evidence is presented which suggests that, in RB samples of moderate sizes, the bias-reduced GMM estimators perform well
- Parametric and semiparametric specification tests for binary choice models : a comparative simulation studyPublication . Proença, Isabel; Silva, João M. Caravana SantosDespite their sensitivity to misspecification, parametric binary choice models are widely used in practice. Here we present the results of a small simulation study on the finite sample performance of parametric and semiparametric specification tests for this kind of models.
- Estimativas 'Jackknif' e 'Bootstrap' para o enviesamento e desvio padrão do índice de GiniPublication . Proença, IsabelNeste trabalho serão apresentados os métodos "Jacknife" e "Bootstrap" Ilustrando-se as suas potencialidades com o exemplo númérico onde se aplicam estas técnicas ao indice de concentração de Gini.
- Profitable mixed capacitated arc routing and related problemsPublication . Benavent, Enrique; Corberán, Ángel; Gouveia, Luís; Mourão, M. Cândida; Pinto, Leonor SantiagoMixed Capacitated Arc Routing Problems (MCARP) aim to identify a set of vehicle trips that, starting and ending at a depot node, serve a given number of links, regarding the vehicles capacity, and minimizing a cost function. If both profits and costs on arcs are considered, the Profitable Mixed Capacitated Arc Routing Problem (PMCARP) may be defined. We present compact flow based models for the PMCARP, where two types of services are tackled, mandatory and optional. Adaptations of the models to fit into some other related problems are also proposed. The models are evaluated, according to their bounds quality as well as the CPU times, over large sets of test instances. New instances have been created from benchmark ones in order to solve variants that have been introduced here for the first time. Results show the new models performance within CPLEX and compare, whenever available, the proposed models against other resolution methods
- Tail index estimation in the presence of covariates : Stock returns’ tail risk dynamicsPublication . Nicolau, João; Rodrigues, Paulo M. M.; Stoykov, Marian Z.This paper provides novel theoretical results for the estimation of the conditional tail index of Pareto and Pareto-type distributions in a time series context. We show that both the estimators and relevant test statistics are normally distributed in the limit, when independent and identically distributed or dependent data are considered. Simulation results provide support for the theoretical findings and highlight the good finite sample properties of the approach in a time series context. The proposed methodology is then used to analyze stock returns’ tail risk dynamics. Two empirical applications are provided. The first consists in testing whether the time-varying tail exponents across firms follow Kelly and Jiang’s (2014) assumption of common firm level tail dynamics. The results obtained from our sample seem not to favour this hypothesis. The second application, consists of the evaluation of the impact of two market risk indicators, V IX and Expected Shortfall (ES) and two firm specific covariates, capitalization and market-to-book on stocks tail risk dynamics. Although all variables seem important drivers of firms’ tail risk dynamics, it is found that overall ES and firms’ capitalization seem to have overall wider impact.
- Identifying common spectral and asymmetric features in stock returnsPublication . Caiado, Jorge; Crato, NunoThis paper proposes spectral and asymmetric-volatility based methods for cluster analysis of stock returns. Using the information about both the periodogram of the squared returns and the estimated parameters in the TARCH equation, we compute a distance matrix for the stock returns. Clusters are formed by looking to the hierarchical structure tree (or dendrogram) and the computed principal coordinates. We employ these techniques to investigate the similarities and dissimilarities between the "blue-chip" stocks used to compute the Dow Jones Industrial Average (DJIA) index. For reference, we investigate also the similarities among stock returns by mean and squared correlation methods.
- Comparison of time series with unequal lengthPublication . Caiado, Jorge; Crato, Nuno; Peña, DanielThe comparison and classification of time series is an important issue in practical time series analysis. For these purposes, various methods have been proposed in the literature, but all have shortcomings, especially when the observed time series have different sample sizes. In this paper, we propose spectral domain methods for handling time series of unequal length. The methods make the spectral estimates comparable, by producing statistics at the same frequency. A first sensible approach may consist on zero-padding the shorter time series in order to increase the corresponding number of periodogram ordinates. We show that this works well provided the sample sizes are not very different, but does not give good results in case the time series lengths are very unbalanced. For this latter case, we study some periodogram-based comparison methods and construct a test. Both the methods and the test display reasonable properties for series of any lengths. Additionally and for reference, we develop a parametric comparison method. The procedures are assessed by a Monte Carlo simulation study. As an illustrative example, a periodogram method is used to compare and cluster industrial production series of some developed countries.
- A GARCH-based method for clustering of financial time series: International stock markets evidencePublication . Caiado, Jorge; Crato, NunoIn this paper, we introduce a volatility-based method for clustering analysis of financial time series. Using the generalized autoregressive conditional heteroskedasticity (GARCH) models we estimate the distances between the stock return volatilities. The proposed method uses the volatility behavior of the time series and solves the problem of different lengths. As an illustrative example, we investigate the similarities among major international stock markets using daily return series with different sample sizes from 1966 to 2006. From cluster analysis, most European markets countries, United States and Canada appear close together, and most Asian/Pacific markets and the South/Middle American markets appear in a distinct cluster. After the terrorist attack on September 11, 2001, the European stock markets have become more homogenous, and North American markets, Japan and Australia seem to come closer.
- A reexamination of inflation persistence dynamics in OECD countries : A new approachPublication . Zsurkis, Gabriel; Nicolau, João; Rodrigues, Paulo M.M.This paper introduces a simple and easy to implement procedure to test for changes in persistence. The time-varying parameter that characterizes persistence changes under the alternative hypothesis is approximated by a parsimonious cosine function. The new test procedure is the minimum of a t-statistic, computed from a test regression that considers a set of reasonable values for a frequency term that is used to evaluate the time varying properties of persistence. The asymptotic distributions of the new tests are derived and critical values are provided. An indepth Monte Carlo analysis shows that the new procedure has important power gains when compared to the local GLS de-trended Dickey-Fuller (DF GLS) type tests introduced by Elliott et al. (1996) under various data generating processes with persistence changes. Moreover, an empirical application to OECD countries’ inflation series shows that for most countries analysed persistence was high in the first half of the sample and subsequently decreased. These results are compatible with modern macroeconomic theories that point to changes in inflation behavior in the early 1980s and also with recent empirical evidence against the I(1)-I(0) dichotomy.
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