Nuno Crato
University of Lisbon, ISEG, Department of Mathematics, Department Member
- Nuno Crato (http://www.nunocrato.org), Ph.D. in Applied Mathematics, has published in the fields of time series analy... moreNuno Crato (http://www.nunocrato.org), Ph.D. in Applied Mathematics, has published in the fields of time series analysis, applied probability models, statistics, econometrics, evaluation, and education. Now professor of Mathematics and Statistics at the University of Lisbon and senior visiting researcher at the EC-JRC in Italy, has worked at Stevens Institute of Technology and NJIT in NJ, U.S. Has served as a dean at the Technical University of Lisbon and president of Taguspark, the largest science and technology park in Portugal.
Portuguese Minister of Education and Science from 2011 to 2015. During these years, compulsory schooling was raised from 9 to 12 school years, mandatory English was introduced starting at 3rd grade, dropout rates were reduced from c. 25% to 13.7%, retention rates improved, and Portuguese students achieved the best results ever in international surveys PISA and TIMSS.
An active science writer and educational essayist, wrote more than a dozen books, some published in the U.K., U.S., Portugal, Brazil, and Italy. For his writings, has received prizes from the European Mathematical Society and the European Union.
-edit - Ph.D. Advisor (1992): Howard M. Taylor, University of Delawareedit
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Abstract: Various authors claim to have found evidence of stochastic long memory behavior in futures' contract returns using the Hurst statistic. This paper reexamines futures' returns for evidence of persistent behavior... more
Abstract: Various authors claim to have found evidence of stochastic long memory behavior in futures' contract returns using the Hurst statistic. This paper reexamines futures' returns for evidence of persistent behavior using a biased-corrected version of the Hurst statistic and an ...
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Most of economic and financial time series have a nonstationary behavior. There are different types of nonstationary processes, such as those with stochastic trend and those with deterministic trend. In practice, it can be quite difficult... more
Most of economic and financial time series have a nonstationary behavior. There are different types of nonstationary processes, such as those with stochastic trend and those with deterministic trend. In practice, it can be quite difficult to distinguish between the two processes. In this paper, we compare random walk and determinist trend processes using sample autocorrelation, sample partial autocorrelation and
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Long-memory processes, such as Autoregressive Fractionally Integrated Moving-Average processes—ARFIMA—are likely to lead the observer to make serious misspecification errors. Nonstationary ARFIMA processes can easily be misspecified as... more
Long-memory processes, such as Autoregressive Fractionally Integrated Moving-Average processes—ARFIMA—are likely to lead the observer to make serious misspecification errors. Nonstationary ARFIMA processes can easily be misspecified as ARIMA models, thus confusing a fractional degree of integration with an integer one. Stationary persistent ARFIMA processes can be misspecified as nonstationary ARIMA models, thus leading to a serious increase of out-of-sample forecast errors. In this paper, we discuss three prototypical misspecification cases and derive the corresponding increase in mean square forecasting error for different lead times.
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We propose and study a new frequency-domain procedure for characterizing and comparing large sets of long time series. Instead of using all the information available from data, which would be computationally very expensive, we propose... more
We propose and study a new frequency-domain procedure for characterizing and comparing large sets of long time series. Instead of using all the information available from data, which would be computationally very expensive, we propose some regulariza-tion rules in order to select and summarize the most relevant information for clustering purposes. Essentially, we suggest to use a fragmented periodogram computed around the driving cyclical components of interest and to compare the various estimates. This procedure is computationally simple, but able to condense relevant information of the time series. A simulation exercise shows that the smoothed fragmented periodogram works in general better than the non-smoothed one and not worse than the complete periodogram for medium to large sample sizes. We illustrate this procedure in a study of the evolution of several stock markets indices. We further show the effect of recent financial crises over these indices behaviour.
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Nonstationary ARIMA processes and nearly nonstationary ARMA pro-cesses, such as autoregressive processes having a root of the AR polynomial close to the unit circle, have sample autocovariance and spectral properties that are, in... more
Nonstationary ARIMA processes and nearly nonstationary ARMA pro-cesses, such as autoregressive processes having a root of the AR polynomial close to the unit circle, have sample autocovariance and spectral properties that are, in practice, almost indistinguishable from those of a stationary long-memory process, such a s a F ractionally Integrated ARMA ARFIMA process. Because of this, model misspeciication may occur in trying to distinguish be-tween the diierent processes. An appealing strategy would be to overspecify the model and estimate the integration parameter. In this paper, we i n v estigate the eeects of this type of misspeciication on parameter estimates using either spectral regression or frequency-domain maximum likelihood methods.
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The choice of the appropriate degree of integration is a very important question in ARIMAtime series modeling. This choice is particularly difficult in the presence of either a nearlynonstationary autoregression or a fractionally... more
The choice of the appropriate degree of integration is a very important question in ARIMAtime series modeling. This choice is particularly difficult in the presence of either a nearlynonstationary autoregression or a fractionally integrated process. Via a Monte Carlo studywe assess the size and power of MA, AR and spectral estimation tests in the presence offractionally integrated, nearly nonstationary, and
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Experimentalists have found stationary long non-periodic waves in human controlled rhythmic movements. For these type of data, namely for tapping tasks, the now-classical Wing-Kristofferson model offers a decomposition of the... more
Experimentalists have found stationary long non-periodic waves in human controlled rhythmic movements. For these type of data, namely for tapping tasks, the now-classical Wing-Kristofferson model offers a decomposition of the inter-response intervals ...
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Previous studies have investigated the comovements of international equity markets by using correlation, cointegration, common factor analysis, and other approaches. In this paper, we investigate the stochastic structure of major euro and... more
Previous studies have investigated the comovements of international equity markets by using correlation, cointegration, common factor analysis, and other approaches. In this paper, we investigate the stochastic structure of major euro and non-euro area stock market series from 1994 to 2006, by using cluster analysis techniques for time series. We use an interpolated-periodogram based metric for level and squared returns
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roots. Abstract: IntheARIMA modeling of business, ¯nan- cial, and macroeconomic time series, a very important question consists on the determination of the degree of integration of the data under analysis. There are essen- tially three... more
roots. Abstract: IntheARIMA modeling of business, ¯nan- cial, and macroeconomic time series, a very important question consists on the determination of the degree of integration of the data under analysis. There are essen- tially three di®erent approaches to this problem. In the ¯rst approach, the analyst tests for underdi®erencing, i.e., for the existence of one or more autoregressive unit roots, in order to decide whether further di®erencing is necessary. In the second approach, the analyst tests for overdi®erencing, i.e., for the existence of a unit root in themoving averagepolynomial of the ARMA model. In the third approach, the analyst directly estimates the degree of integration of the time series via spectral or time-domainmethods. Inthispaper,weprovideaMonte Carlo comparisonof thesethreedi®erent approaches. In particular, wecontrastthepower of thedi®erent tests in fractionally integrated and in nearly nonstationary and nearly noninvertible processes.
Research Interests: Time Series and Unit Root
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Time series displaying long-range correlations have been observed in numerous fields, such as biology, psychology, hydrology, and economics, among others. For rhythmic movements such as tapping tasks, the Wing–Kristofferson model offers a... more
Time series displaying long-range correlations have been observed in numerous fields, such as biology, psychology, hydrology, and economics, among others. For rhythmic movements such as tapping tasks, the Wing–Kristofferson model offers a decomposition of ...
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The choice of the appropriate degree of integration is a very important question in ARIMAtime series modeling. This choice is particularly difficult in the presence of either a nearlynonstationary autoregression or a fractionally... more
The choice of the appropriate degree of integration is a very important question in ARIMAtime series modeling. This choice is particularly difficult in the presence of either a nearlynonstationary autoregression or a fractionally integrated process. Via a Monte Carlo studywe assess the size and power of MA, AR and spectral estimation tests in the presence offractionally integrated, nearly nonstationary, and
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Invited presentation for the opening of MS in Quantitative Economic Analysis – Universidad Autonoma de Madrid, 19 September 2022
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Clustering time series may bring information about a set of time series and help forecasting or nowcasting a particular series of interest. Such procedures maybe particularly interesting but difficult in a big-data environment. We propose... more
Clustering time series may bring information about a set of time series and help forecasting or nowcasting a particular series of interest. Such procedures maybe particularly interesting but difficult in a big-data environment. We propose and study a frequency-domain procedure for characterizing and comparing large sets of long financial time series volatility. Instead of using all the information available from data, which would be computationally very expensive, we propose to select and summarize the most relevant information for clustering purposes. Essentially, we propose to use a fragmented periodogram, computed only at the driving seasonal components of interest. This procedure is computationally simple, but able to condense relevant second-order information to compare and cluster the volatility time series. We use this procedure to study the evolution of several stock markets indices, extracting information both on the European financial integration and on the recent worldwide financial crisis.
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National administrations, European institutions and public organisations collect, supervise, and keep track of extremely varied and extensive types of data. Modern technologies and better organized civil lives have facilitated the... more
National administrations, European institutions and public organisations collect, supervise, and keep track of extremely varied and extensive types of data. Modern technologies and better organized civil lives have facilitated the collection and custody of these data on a scale previously unknown. This opens novel perspectives to our daily lives, but also allows for a much more detailed and sound knowledge of our economies and our societies. In what follows, I will deal with an important issue within this general framework: the case for the collection, treatment, availability and use of micro-data, in particular administrative data (admin-data). I will urge to take action on the use of these data for a better, easier and more cost-effective evaluation of policies. In fact, there is already an incredible wealth of available data that opens the door to a better knowledge of our economies and our societies. If these data are well kept, organized, complemented, and linked, if data are regularly updated and used for the knowledge of the economic and social situation, if policy measures are recurrently evaluated and adjusted on the basis of this information, and if appropriate scientific methods are used, then our societies can make a better use of their resources and our policy measures can be more efficient. At a moment of increasing attention to the efficacy of public spending, of increasing scrutiny over the effects of policies, it is more important than ever to be able to understand our society and to know how policy measures are impacting over our lives. We have the data, we have the means, and we have the necessary scientific methods. We have to do it.
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This open access book compares and contrasts the results of international student assessments in ten countries. The OECD’s Programme for International Student Assessment (PISA) released the results of its 2018 assessment in December 2019.... more
This open access book compares and contrasts the results of international student assessments in ten countries. The OECD’s Programme for International Student Assessment (PISA) released the results of its 2018 assessment in December 2019. This book reflects the debates that typically follow the release of these results and focuses on the causes of differences between countries. Such causes include continuous decline in one country, improvement combined with increasing internal inequalities in another country, or rapid improvement in spite of an outdated curriculum in yet another.
In addition, the book discusses a number of general questions: Is knowledge outdated? Are computers taking over and replacing teachers? Are schools killing creativity? Are we adequately preparing the next generation? Are schools failing to educate our kids? The book starts out with a summary of PISA’s evolution and PISA results, and an explanation of the major factors that play a role in changes in countries’ results. The next ten chapters are devoted to ten specific countries, offering a summary of data and an explanation of the major drives for changes in education results for each one. Each chapter includes a short description of the country’s educational system as well as the impact of PISA and other ILSA studies on the country’s educational policies. The chapters also include a timeline of policy measures and main hallmarks of the country’s educational evolution, discussing the impact of these measures on its PISA results. A final reference chapter explains what PISA is, what it measures and how. While highlighting the 2018 results, the book also takes into consideration previous results, as well as long-term initiatives.
This book gathers the contribution of well-known and respected experts in the field. Specialists such as Eric Hanushek, for the US, Tim Oates, for England, Montse Gomendio, for Spain, Gunda Tire, for Estonia, and all other contributors draw on their vast experience and statistical analysis expertise to draw a set of rich country lessons and recommendations that are invaluable for all of those who care about improving a country’s education system.
In addition, the book discusses a number of general questions: Is knowledge outdated? Are computers taking over and replacing teachers? Are schools killing creativity? Are we adequately preparing the next generation? Are schools failing to educate our kids? The book starts out with a summary of PISA’s evolution and PISA results, and an explanation of the major factors that play a role in changes in countries’ results. The next ten chapters are devoted to ten specific countries, offering a summary of data and an explanation of the major drives for changes in education results for each one. Each chapter includes a short description of the country’s educational system as well as the impact of PISA and other ILSA studies on the country’s educational policies. The chapters also include a timeline of policy measures and main hallmarks of the country’s educational evolution, discussing the impact of these measures on its PISA results. A final reference chapter explains what PISA is, what it measures and how. While highlighting the 2018 results, the book also takes into consideration previous results, as well as long-term initiatives.
This book gathers the contribution of well-known and respected experts in the field. Specialists such as Eric Hanushek, for the US, Tim Oates, for England, Montse Gomendio, for Spain, Gunda Tire, for Estonia, and all other contributors draw on their vast experience and statistical analysis expertise to draw a set of rich country lessons and recommendations that are invaluable for all of those who care about improving a country’s education system.
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This book is open access under a CC BY 4.0 license. In the light of better and more detailed administrative databases, the book provides statistical tools for evaluating the effects of public policies advocated by governments and public... more
This book is open access under a CC BY 4.0 license.
In the light of better and more detailed administrative databases, the book provides statistical tools for evaluating the effects of public policies advocated by governments and public institutions. Experts from academia, national statistics offices and various research centers present modern econometric methods for an efficient data-driven policy evaluation and monitoring, assess the causal effects of policy measures and report on best practices of successful data management and usage.
Topics include data confidentiality, data linkage, and national practices in policy areas such as public health, education and employment. It offers scholars as well as practitioners from public administrations, consultancy firms and nongovernmental organizations insights into counterfactual impact evaluation methods and the potential of data-based policy and program evaluation.
In the light of better and more detailed administrative databases, the book provides statistical tools for evaluating the effects of public policies advocated by governments and public institutions. Experts from academia, national statistics offices and various research centers present modern econometric methods for an efficient data-driven policy evaluation and monitoring, assess the causal effects of policy measures and report on best practices of successful data management and usage.
Topics include data confidentiality, data linkage, and national practices in policy areas such as public health, education and employment. It offers scholars as well as practitioners from public administrations, consultancy firms and nongovernmental organizations insights into counterfactual impact evaluation methods and the potential of data-based policy and program evaluation.
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A briefing on the importance of administrative data for social knowledge and policy evaluation, at Big Data times A call to action for better data and better policy evaluation 2017 EUR 28434 EN
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Marco Tropea, Milano, 2011
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A divulgação científica é uma das actividades culturais mais importantes na sociedade moderna. Em nada sai diminuída de um contraste com o ensino e a investigação, e de forma alguma fica apoucada pela delimitação das suas características... more
A divulgação científica é uma das actividades culturais mais importantes na sociedade moderna. Em nada sai diminuída de um contraste com o ensino e a investigação, e de forma alguma fica apoucada pela delimitação das suas características e possibilidades. Se se limitar a informar o público interessado de tópicos importantes da ciência actual, se acrescentar a isso referências e gosto pelo conhecimento, estará já a desempenhar um papel decisivo para o progresso do país. Mas a divulgação e o jornalismo científico podem ainda trazer a ciência para o palco da vida cultural, mostrando que esta é parte da vida e parte da cultura. Esta actividade, por si só, é suficientemente nobre para a tornar imprescindível na sociedade moderna. Se olharmos a divulgação desta forma, compará-la com o ensino ou com a investigação científica será tão fastidioso como bizarro. A divulgação científica não necessita de extravasar o seu âmbito e os seus objectivos para assumir na sociedade moderna o papel nobre que merece.
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In this paper, I provide an overview of the recent evolution of Portuguese students' results in elementary and middle school mathematics. I highlight the reforms slowly introduced from 2003 to 2015, and their results. These reforms were... more
In this paper, I provide an overview of the recent evolution of Portuguese students' results in elementary and middle school mathematics. I highlight the reforms slowly introduced from 2003 to 2015, and their results. These reforms were pragmatic and made in response to the poor results obtained by Portuguese students in the early TIMSS and PISA studies and got a significant and deliberate boost in 2011, when the government invited experts from the Portuguese Mathematical Society to collaborate on new programs and standards. Results from both PISA and TIMSS after the application of the new standards showed a significant improvement, with 4th grade Portuguese students passing their counterparts from traditionally better performing countries, such as Finland. Subsequent abolition of the new standards and other reforms of the period led to a significant backslide of the educational panorama. However, only now the news of Portuguese successes is spreading, and we must look at what has determined the advances and regressions. In order to understand what leads to good education results, we need to look at what a country did, and not at what it is doing now.
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Entre as últimas décadas do século XX e as duas primeiras do século XXI, Portugal foi palco de várias reformas que mudaram a política educativa de uma visão romântica para um esforço consciente de melhoria dos conhecimentos e capacidades... more
Entre as últimas décadas do século XX e as duas primeiras do século XXI, Portugal foi palco de várias reformas que mudaram a política educativa de uma visão romântica para um esforço consciente de melhoria dos conhecimentos e capacidades dos alunos. Esse esforço teve frutos, e em 2015 os estudantes portugueses registaram os seus melhores resultados de sempre nas avaliações internacionais PISA e TIMSS. Infelizmente, essa orientação e esse esforço estão a ser revertidos e os resultados são preocupantes.
O que se deve fazer é claro: instituir um currículo estruturado e ambicioso, em paralelo com um sistema de avaliação que permita ir seguindo os progressos e corrigindo as deficiências.
O que se deve fazer é claro: instituir um currículo estruturado e ambicioso, em paralelo com um sistema de avaliação que permita ir seguindo os progressos e corrigindo as deficiências.
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Apresentação de encerramento no Física 2022, encontro da Sociedade Portuguesa de Física na Universidade do Porto. A ciência moderna valoriza as disciplinas, o currículo estruturado e o conhecimento. Recomenda um ensino ativo, mas ativo... more
Apresentação de encerramento no Física 2022, encontro da Sociedade Portuguesa de Física na Universidade do Porto.
A ciência moderna valoriza as disciplinas, o currículo estruturado e o conhecimento. Recomenda um ensino ativo, mas ativo mentalmente. Recomenda projetos, mas não basear o ensino em projetos. Recomenda o respeito pelo aluno, mas não seguir os instintos dos alunos.
No ensino da Física, essa ciência tão fundamental, é decisivo seguir estas recomendações das ciências cognitivas e dos estudos estatísticos modernos.
A ciência moderna valoriza as disciplinas, o currículo estruturado e o conhecimento. Recomenda um ensino ativo, mas ativo mentalmente. Recomenda projetos, mas não basear o ensino em projetos. Recomenda o respeito pelo aluno, mas não seguir os instintos dos alunos.
No ensino da Física, essa ciência tão fundamental, é decisivo seguir estas recomendações das ciências cognitivas e dos estudos estatísticos modernos.
Cómo mejorar la educación de un país Concéntrate en los fundamentos: - Currículo exigente: conocimientos (y competencias) - Evaluación rigurosa - Apoyar a todos los estudiantes sin bajar los estándares Las políticas educativas deben ser... more
Cómo mejorar la educación de un país
Concéntrate en los fundamentos:
- Currículo exigente: conocimientos (y competencias)
- Evaluación rigurosa
- Apoyar a todos los estudiantes sin bajar los estándares
Las políticas educativas deben ser juzgadas por
resultados de los estudiantes, y no por intenciones políticas.
Concéntrate en los fundamentos:
- Currículo exigente: conocimientos (y competencias)
- Evaluación rigurosa
- Apoyar a todos los estudiantes sin bajar los estándares
Las políticas educativas deben ser juzgadas por
resultados de los estudiantes, y no por intenciones políticas.
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Contrarily to very spread speculations, International Large Scale Assessment studies such as PISA and TIMSS do not point towards the need of having a vague competences-based curriculum nor towards the advantage of discovery-learning... more
Contrarily to very spread speculations, International Large Scale Assessment studies such as PISA and TIMSS do not point towards the need of having a vague competences-based curriculum nor towards the advantage of discovery-learning methods, nor even towards the need to make the curricular standards more flexible in order to "reduce inequalities". PISA and TIMSS study results support the need of a ambitious standards, teacher-directed explicit instruction, and frequent assessment.
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PISA 2018 was the largest large-scale international assessment to date. Its results confirm the improvements of some countries, the challenges other countries face, and the decline observed in a few others. This chapter reflects on the... more
PISA 2018 was the largest large-scale international assessment to date. Its results confirm the improvements of some countries, the challenges other countries face, and the decline observed in a few others. This chapter reflects on the detailed analyses of ten countries policies, constraints, and evolutions. It highlights key factors, such as investment, curriculum, teaching, and student assessment. And it concludes by arguing that curriculum coherence, an emphasis on knowledge, student observable outcomes, assessment, and public transparency are key elements. These elements are crucial both for education success in general and for its reflection on PISA and other international assessments.
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This chapter provides a short description of what the Programme for International Student Assessment (PISA) measures and how it measures it. First, it details the concepts associated with the measurement of student performance and the... more
This chapter provides a short description of what the Programme for International Student Assessment (PISA) measures and how it measures it. First, it details the concepts associated with the measurement of student performance and the concepts associated with capturing student and school characteristics and explains how they compare with some other International Large-Scale Assessments (ILSA). Second, it provides information on the assessment of reading, the main domain in PISA 2018. Third, it provides information on the technical aspects of the measurements in PISA. Lastly, it offers specific examples of PISA 2018 cogni-tive items, corresponding domains (mathematics, science, and reading), and related performance levels.
How ambitious curricula, aligned assessment, and focus on all students improved education in Portugal until 2015
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I sustain that good national results need a good and clear curriculum, aligned quality materials, students’ regular assessment, support to all, vocational paths, and flexibility
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A few months after becoming minister, I used to say that “no one who has never before been an education minister should ever become an education minister”. This silly joke wasn’t usually understood. But what I meant was clear to me: this... more
A few months after becoming minister, I used to say that “no one who has never before been an education minister should ever become an education minister”. This silly joke wasn’t usually understood. But what I meant was clear to me: this is the type of job for which we are always unprepared.
How can someone who has the advantage of having had such an experience be useful to those who are initiating it? Maybe by listing a few recommendations that for the very same person, i.e., me, have proven to be more important than I thought.
How can someone who has the advantage of having had such an experience be useful to those who are initiating it? Maybe by listing a few recommendations that for the very same person, i.e., me, have proven to be more important than I thought.
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By the turn of the century, following the dismal first results in TIMSS and PISA, the Portuguese educational system was at a crossroads. It was clear that students were not attaining minimal levels of proficiency in reading, math,... more
By the turn of the century, following the dismal first results in TIMSS and PISA, the Portuguese educational system was at a crossroads. It was clear that students were not attaining minimal levels of proficiency in reading, math, science, and other basic subjects. The system needed a deep reshaping, and so changes were made. By the time the last PISA and TIMSS international large-scale surveys' results were released in 2015, Portugal registered a quantum leap: in PISA, student achievement was above the OECD average and in TIMSS, 4th graders had higher scores in Mathematics than several usually high-performing countries, including Finland. How was this possible? To understand what happened, we need to look at what Portugal has done in the last 10-15 years. Although many different ministers from different ideological standpoints made different reforms, there is a common thread to most changes: they paid increased attention to results. This proved to be a powerful thrust for improvement, backed up by experienced teachers. However, this general thrust assumed many concrete different aspects and promoted different reforms. During the 2011-2015 period, these reforms went further and were very clear, intentional, and explicit: a clear curriculum, increased school autonomy, stu-dents' regular assessment, vocational paths, flexibility. All this helped to prepare youngsters for an active, productive, and responsible life in the twenty-first century.
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A comienzos de siglo, tras los deplorables resultados obtenidos en las primeras pruebas TIMSS y PISA, el sistema educativo portugués se encontraba en una encrucijada. Claramente, el alumnado no estaba alcanzando los niveles mínimos de... more
A comienzos de siglo, tras los deplorables resultados obtenidos en las primeras pruebas TIMSS y PISA, el sistema educativo portugués se encontraba en una encrucijada. Claramente, el alumnado no estaba alcanzando los niveles mínimos de competencia en comprensión lectora, matemáticas, ciencias y otras materias básicas. El sistema necesitaba una remodelación profunda, de modo que se realizaron cambios. En 2015, cuando se publicaron los últimos resultados de las pruebas internacionales PISA y TIMSS, Portugal registró un salto cuantitativo: en PISA, los resultados del alumnado se situaron por encima de la media de la OCDE; y en TIMSS, los alumnos de cuarto curso alcanzaron puntuaciones más altas en matemáticas que varios países con resultados habitualmente altos, como Finlandia. ¿Cómo se logró este avance? Para entender qué había ocurrido, necesitamos observar lo que Portugal ha hecho en los últimos 10 o 15 años. Aunque muchos ministros de diferentes ideologías llevaron a cabo diversas reformas, la mayoría de los cambios siguieron un hilo común: prestaban cada vez más atención a los resultados. Esto acabó dando un enorme impulso a la mejora, respaldado por docentes experimentados. Sin embargo, este impulso general asumió muchos aspectos concretos diferentes, y dio pie a reformas distintas. Durante el periodo 2011-2015, las reformas llegaron más lejos, y fueron muy claras, intencionales y explícitas: un plan de estudios claro, mayor autonomía de los centros educativos, evaluación regular del alumnado, itinerarios de formación profesional, flexibilidad. Todo esto ayudó a preparar a los jóvenes para una vida activa, productiva y responsable en el siglo XXI.
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RESUMO: A recente pandemia tornou evidentes para quase todos nós as grandes vantagens do ensino presencial e as grandes limitações do ensino remoto. Mas vale a pena revisitar um pouco as ilusões que estavam por detrás de alguma... more
RESUMO: A recente pandemia tornou evidentes para quase todos nós as grandes vantagens do ensino presencial e as grandes limitações do ensino remoto. Mas vale a pena revisitar um pouco as ilusões que estavam por detrás de alguma encomiástica defesa do ensino remoto, pois esse debate, que hoje encontra suporte em dados científicos, pode levar-nos a melhorar tanto o ensino presencial como a minorar inconvenientes do ensino remoto. Essa melhoria é tanto mais importante quanto a pandemia nos trouxe atrasos ou mesmo retrocessos no esforço educativo. Com base em investigação científica muito recente, defende-se neste artigo que a resposta aos inconvenientes da pandemia não pode ser apenas manter os estudantes ocupados e em contacto com a escola e a aprendizagem. A resposta deve ser acelerar o ritmo e a qualidade da educação. Para o fazer, é ainda mais importante prosseguir um currículo exigente e ambicioso e proceder a uma avaliação de resultados frequente e rigorosa. Os meios remotos podem ser um complemento valioso do ensino presencial.
PALAVRAS-CHAVE: Ensino híbrido; ensino remoto digital; pandemia; romantismo digital
ABSTRACT: The pandemic made visible both the great advantages of face-to-face teaching and the great disadvantages of remote learning. It is nevertheless interesting to revisit a few illusions behind some hagiographic defence of remote learning. Today, this debate can be supported by scientific evidence and it can lead to improvements both in the face-to-face and in the remote teaching. These improvements are more than necessary at this moment, as the pandemic brought about serious delays in the learning processes. With support on recent scientific research, this paper sustains that the answer to the pandemic cannot be to just keep students in contact with school activities. The answer ought to be to accelerate the educational pace and to improve the educational quality. For this purpose, we need an ambitious and rigorous curriculum and frequent and reliable student evaluations. Remote learning should not be separated from the general learning process but integrated in it and seen as a complement to face-to-face schooling.
Keywords: Blended learning, digital remote teaching, digital romanticism, pandemic
PALAVRAS-CHAVE: Ensino híbrido; ensino remoto digital; pandemia; romantismo digital
ABSTRACT: The pandemic made visible both the great advantages of face-to-face teaching and the great disadvantages of remote learning. It is nevertheless interesting to revisit a few illusions behind some hagiographic defence of remote learning. Today, this debate can be supported by scientific evidence and it can lead to improvements both in the face-to-face and in the remote teaching. These improvements are more than necessary at this moment, as the pandemic brought about serious delays in the learning processes. With support on recent scientific research, this paper sustains that the answer to the pandemic cannot be to just keep students in contact with school activities. The answer ought to be to accelerate the educational pace and to improve the educational quality. For this purpose, we need an ambitious and rigorous curriculum and frequent and reliable student evaluations. Remote learning should not be separated from the general learning process but integrated in it and seen as a complement to face-to-face schooling.
Keywords: Blended learning, digital remote teaching, digital romanticism, pandemic
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O sucesso educativo é mais simples do que parece!? Sim, se esquecermos as soluções falsas, complicadas e que se dizem milagrosas e nos concentrarmos naquilo que a ciência, a experiência e o bom senso nos dizem: currículo, avaliação,... more
O sucesso educativo é mais simples do que parece!? Sim, se esquecermos as soluções falsas, complicadas e que se dizem milagrosas e nos concentrarmos naquilo que a ciência, a experiência e o bom senso nos dizem: currículo, avaliação, incentivos certos, apoios aos alunos nas primeiras dificuldades, autonomia das escolas e vias alternativas para os estudantes no Secundário. Nesta apresentação defende-se que tudo começa no currículo. Destruí-lo ou abastardá-lo conduz ao insucesso.
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Apresentação convidada na Escola de Verão da Sociedade Portuguesa de Matemática em 3 de Julho de 2019. Procuro mostrar como o conhecimento científico moderno apoia um ensino estruturado e revela os prejuízos de privilegiar o chamado... more
Apresentação convidada na Escola de Verão da Sociedade Portuguesa de Matemática em 3 de Julho de 2019.
Procuro mostrar como o conhecimento científico moderno apoia um ensino estruturado e revela os prejuízos de privilegiar o chamado 'ensino pela descoberta'
Procuro mostrar como o conhecimento científico moderno apoia um ensino estruturado e revela os prejuízos de privilegiar o chamado 'ensino pela descoberta'
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Instead of talking about vague "twenty-first-century competencies", this presentation discusses a few scientific results from statistical analysis of education and from cognitive psychology that are available and constitute... more
Instead of talking about vague "twenty-first-century competencies", this presentation discusses a few scientific results from statistical analysis of education and from cognitive psychology that are available and constitute twenty-first-century tools for improving education.
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Intervenção na sessão da "Exame"-Grupo Abril e da fundação "Todos pela Educação" em São Paulo, abrindo o debate com os candidatos a Presidente do Brasil sobre a política educativa que preconizam. A apresentação discute os motivos... more
Intervenção na sessão da "Exame"-Grupo Abril e da fundação "Todos pela Educação" em São Paulo, abrindo o debate com os candidatos a Presidente do Brasil sobre a política educativa que preconizam. A apresentação discute os motivos essenciais que levaram Portugal a melhorar o sistema educativo até ultrapassar a média da OCDE no PISA 2015 e a própria Finlândia em matemática do 4.º ano de escolaridade no TIMSS 2015. Defende-se que os factores essenciais giram em torno de um ensino mais exigente e bem estruturado com metas precisas e de uma melhor e mais frequente avaliação externa dos alunos.
Presentation (in Portuguese) at the "Exame"-Grupo Abril magazine and Todos pela Educação foundation in São Paulo, Brazil, opening the debate with presidential candidates to upcoming elections on their education policy. The presentation supported the description of the factors that improved Portuguese educational system to the point of surpassing the OECD average in PISA 2015 and even Finland in math 4th grade in TIMSS 2015. It makes the case for a more demanding, better structured and more precise curriculum a par with a more frequent external student evaluation.
Presentation (in Portuguese) at the "Exame"-Grupo Abril magazine and Todos pela Educação foundation in São Paulo, Brazil, opening the debate with presidential candidates to upcoming elections on their education policy. The presentation supported the description of the factors that improved Portuguese educational system to the point of surpassing the OECD average in PISA 2015 and even Finland in math 4th grade in TIMSS 2015. It makes the case for a more demanding, better structured and more precise curriculum a par with a more frequent external student evaluation.
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Textbooks have played an important role in the remarkable increase of student's results in Portugal during the last few years. There was an evolution towards a more demanding and rigorous curriculum, which was supported with better... more
Textbooks have played an important role in the remarkable increase of student's results in Portugal during the last few years. There was an evolution towards a more demanding and rigorous curriculum, which was supported with better textbooks. The analysis and certification of textbooks was an important piece in this progress.
But textbooks support a curriculum: if we mistakenly forget the crucial and basic role of knowledge in education, then we could forget the importance of textbooks.
But textbooks support a curriculum: if we mistakenly forget the crucial and basic role of knowledge in education, then we could forget the importance of textbooks.
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... Nuno Crato2 ... Os cálculos de Gauss forneceram estimativas para a órbita de Ceres com pre-cisão suficiente para o astrónomo húngaro Franz Xaver von Zach, na altura di-rector do Observatório de Seeburgo o redescobrir a 31 de Dezembro... more
... Nuno Crato2 ... Os cálculos de Gauss forneceram estimativas para a órbita de Ceres com pre-cisão suficiente para o astrónomo húngaro Franz Xaver von Zach, na altura di-rector do Observatório de Seeburgo o redescobrir a 31 de Dezembro de 1801, praticamente um ano ...
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We analyze the distribution of computational effort required by backtracking algorithms on unsatisfiable CSPs, using analogies with reliability models, where lifetime of a specimen before failure corresponds to the runtime of backtracking... more
We analyze the distribution of computational effort required by backtracking algorithms on unsatisfiable CSPs, using analogies with reliability models, where lifetime of a specimen before failure corresponds to the runtime of backtracking on unsatisfiable CSPs. We ...
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... Tycho Brahe utilizava m ªetodos estatªısticos rudimentares, ho j e consider-ados primitivos. ... Se, a certo momento, por exemplo, tirava cinco medidas da altura de uma estrela como sendo, em graus, 23, 23, 24, 25 e 25, dizia que a... more
... Tycho Brahe utilizava m ªetodos estatªısticos rudimentares, ho j e consider-ados primitivos. ... Se, a certo momento, por exemplo, tirava cinco medidas da altura de uma estrela como sendo, em graus, 23, 23, 24, 25 e 25, dizia que a altura era 24 graus, mais grau menos grau. ...
... comunicação para audiências não científicas 2.ª Aula 13 de Abril (Ana Moutinho) A comunicação com os media ▪ Jornalismo de ciência; funcionamento de uma redacção. ▪ Géneros jornalísticos: notícia, reportagem, entrevista ...
... Ficamo-nos pelo «Bolonhês»? by Nuno Crato. ... Related research. A responsabilidade pelo desenvolvimento. Rosa Maria Fischer, Cristina Fedato, Maria Elidia Souza De Novaes in Conferência Internacional ISTR (2004). 1 reader ...
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Mestrado em Métodos Matemáticos para Gestão de Empresa
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Research Interests: Geography and Portuguese
Jackson Pollock (1912–1956) is well known for his gigantic pictures that combine colored lines, splashes of paint, extensive spirals and rhythmical tracks. But he is just as well known for the controversy his art has generated. Some... more
Jackson Pollock (1912–1956) is well known for his gigantic pictures that combine colored lines, splashes of paint, extensive spirals and rhythmical tracks. But he is just as well known for the controversy his art has generated. Some people have asserted that a monkey could paint more interesting pictures than Pollock’s, or have commented that it is impossible to tell the difference between his pictures and completely random scrawls. How could this man have consciously created such strange, chaotic pictures?
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In this work, we analyze the long-range dependence parameter for a nucleotide sequence in several different transformations. The long-range dependence parameter is estimated by the approximated maximum likelihood method, by a novel... more
In this work, we analyze the long-range dependence parameter for a nucleotide sequence in several different transformations. The long-range dependence parameter is estimated by the approximated maximum likelihood method, by a novel estimator based on the spectral envelope theory, by a regression method based on the periodogram function, and also by the detrended fluctuation analysis method. We study the length distribution of coding and noncoding regions for all Homo sapiens chromosomes available from the European Bioinformatics Institute. The parameter of the tail rate decay is estimated by the Hill estimator ˆα. We show that the tail rate decay is greater than 2 for coding regions, while for almost all noncoding regions it is less than 2.
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Trânsitos de Vénus: À Procura da Escala Exacta do Sistema Solar é um livro fascinante. Conta a história da descoberta dos trânsitos de Vénus e de Mercúrio e explica o que são essas passagens visuais dos planetas entre nós e o Sol. Explica... more
Trânsitos de Vénus: À Procura da Escala Exacta do Sistema Solar é um livro fascinante. Conta a história da descoberta dos trânsitos de Vénus e de Mercúrio e explica o que são essas passagens visuais dos planetas entre nós e o Sol. Explica a dinâmica celeste desses fenómenos raros, fáceis de observar desde que se esteja para isso preparado. A história começa com Kepler, passa por Halley e pelo Capitão Cook. Refere astrónomos de génio e aventureiros. Conta com o contributo de Teodoro de Almeida, Soares de Barros e outros portugueses, como é aqui revelado com base em vária investigação histórica original.
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The present paper discusses the stochastic stationarity of New Zealand exchange rates in light of new time series methods and new tests. The question of whether the real exchange rates have a unit root or are mean reverting is set in the... more
The present paper discusses the stochastic stationarity of New Zealand exchange rates in light of new time series methods and new tests. The question of whether the real exchange rates have a unit root or are mean reverting is set in the general framework of fractionally integrated models. The estimates sustain the claim that New Zealand real exchange series are not stationary. However, it is shown that nonstationarity is compatible with parity reversion in the framework of fractional unit-root models.
This chapter provides a short description of what the Programme for International Student Assessment (PISA) measures and how it measures it. First, it details the concepts associated with the measurement of student performance and the... more
This chapter provides a short description of what the Programme for International Student Assessment (PISA) measures and how it measures it. First, it details the concepts associated with the measurement of student performance and the concepts associated with capturing student and school characteristics and explains how they compare with some other International Large-Scale Assessments (ILSA). Second, it provides information on the assessment of reading, the main domain in PISA 2018. Third, it provides information on the technical aspects of the measurements in PISA. Lastly, it offers specific examples of PISA 2018 cognitive items, corresponding domains (mathematics, science, and reading), and related performance levels.
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A GARCH-based method for clustering of financial time series: International stock markets evidence
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Abstract: This paper proposes an asymmetric-volatility based method for cluster analysis of stock returns. Using the information about the estimated parameters in the TARCH equation, we compute a distance matrix for the stock returns.... more
Abstract: This paper proposes an asymmetric-volatility based method for cluster analysis of stock returns. Using the information about 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.
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Abstract: Previous studies have investigated the comovements of international equity returns by using mean correlations, cointegration, common factor analysis, and other approaches. This paper investigates the evolution of the a ¢ nity... more
Abstract: Previous studies have investigated the comovements of international equity returns by using mean correlations, cointegration, common factor analysis, and other approaches. This paper investigates the evolution of the a ¢ nity among major euro and non-euro area stock markets in the period 1966-2006 by using distance-based methods for clustering analysis of time series. A periodogram-based metric for mean and squared returns is used to compute distances between the series. This method solves the shortcoming of unequal sample sizes found for di¤erent countries. Then, by using dendrogram and multidimensional scaling techniques based on the computed distances, we display clusters for the series of returns and volatilities. The data were divided into two sample periods: previous and subsequent to the introduction of the euro as an electronic currency. For market returns, euro-area countries do not seem to come closer after the introduction of the euro. There is some identity tha...
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PISA 2018 was the largest large-scale international assessment to date. Its results confirm the improvements of some countries, the challenges other countries face, and the decline observed in a few others. This chapter reflects on the... more
PISA 2018 was the largest large-scale international assessment to date. Its results confirm the improvements of some countries, the challenges other countries face, and the decline observed in a few others. This chapter reflects on the detailed analyses of ten countries policies, constraints, and evolutions. It highlights key factors, such as investment, curriculum, teaching, and student assessment. And it concludes by arguing that curriculum coherence, an emphasis on knowledge, student observable outcomes, assessment, and public transparency are key elements. These elements are crucial both for education success in general and for its reflection on PISA and other international assessments.
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Taiwan has, from 2006, participated in five Programme for International Student Assessment (PISA) surveys. This chapter discusses Taiwan’s performance in PISA and its implications. At first, the education system and the process of... more
Taiwan has, from 2006, participated in five Programme for International Student Assessment (PISA) surveys. This chapter discusses Taiwan’s performance in PISA and its implications. At first, the education system and the process of educational reform in Taiwan were described. Then Taiwan’s performances for reading, math, and science in PISA were delineated. Taiwanese students have had consistently excellent performance for math and science; its reading performance, although not as outstanding as those for math and science, has improved significantly from 2009 to 2018. The gender gap in reading, in favour of female students, has narrowed, and the gender gap in math and science has been small. Educational equity, especially between rural and urban students, has also improved from 2006 to 2018. The proportion of high performers in reading and the proportion of low performers in reading, math, and science has increased from 2006 to 2018, while the proportions of top performers in math an...
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Nonstationary ARIMA processes and nearly nonstationary ARMA processes, such as autoregressive processes having a root of the AR polynomial close to the unit circle, have sample autocovariance and spectral properties that are, in practice,... more
Nonstationary ARIMA processes and nearly nonstationary ARMA processes, such as autoregressive processes having a root of the AR polynomial close to the unit circle, have sample autocovariance and spectral properties that are, in practice, almost indistinguishable from those of a stationary longmemory process, such as a Fractionally Integrated ARMA (ARFIMA) process. Because of this, model misspeci cation may occur in trying to distinguish between the di erent processes. An appealing strategy would be to overspecify the model and estimate the integration parameter. In this paper, we investigate the e ects of this type of misspeci cation on parameter estimates using either spectral regression or frequency-domain maximum likelihood methods.
Periodogram analysis has been a standard tool in stationary time series analysis. More recently, with the interest in long-memory fractionally differenced models, periodogram regression methods have been suggested to estimate the degree... more
Periodogram analysis has been a standard tool in stationary time series analysis. More recently, with the interest in long-memory fractionally differenced models, periodogram regression methods have been suggested to estimate the degree of integration of a stationary time series. Let (εt) be a white noise, i.e., an uncorrelated zero-mean process: E εt = 0 and E εt = σ 2 ε , for all t and E εt εt+h = 0 for all h 6= 0. Let B represent the backwards shift operator, i.e., BXt = Xt, and let ∇ = 1 − B represent the differencing operator. For d ∈ (−.5, .5) the process (Xt) is said to be a fractional noise if
Combinatorial search methods often exhibit a large variability in performance. We study the cost prooles of combinatorial search procedures. Our study reveals some intriguing properties of such cost prooles. The distributions are often... more
Combinatorial search methods often exhibit a large variability in performance. We study the cost prooles of combinatorial search procedures. Our study reveals some intriguing properties of such cost prooles. The distributions are often characterized by very long tails or \heavy tails". We will show that these distributions are best characterized by a general class of distributions that have no moments (i.e., an innnite mean, variance , etc.). Such non-standard distributions have recently been observed in areas as diverse as economics, statistical physics, and geophysics. They are closely related to fractal phenomena, whose study was introduced by Mandelbrot. We believe this is the rst nding of these distributions in a purely computational setting. We also show how random restarts can effectively eliminate heavy-tailed behavior, thereby dramatically improving the overall performance of a search procedure. This paper has not already been accepted by and is not currently under rev...
This paper proposes an asymmetric-volatility based method for cluster analysis of stock returns. Using the information about the estimated parameters in the TARCH equation, we compute a distance matrix for the stock returns. Clusters are... more
This paper proposes an asymmetric-volatility based method for cluster analysis of stock returns. Using the information about 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.
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... Nuno Crato Gradiva Publicações, 2006 Autor da resenha: Antonio Luiz Pereira ... O texto é bastanteclaro e procura elucidar, em linguagem simples, afirmações e conceitos que aparecem freqüentemente obscurecidos por pesado jargão - daí... more
... Nuno Crato Gradiva Publicações, 2006 Autor da resenha: Antonio Luiz Pereira ... O texto é bastanteclaro e procura elucidar, em linguagem simples, afirmações e conceitos que aparecem freqüentemente obscurecidos por pesado jargão - daí o “eduquês” do título. ...
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Research Interests: Engineering, Psychophysics, Computer Science, Cognition, Time Series, and 15 moreMotor Control, Fractals, Medicine, Human Movement Science, Stochastic processes, Brain, Humans, Variability, Theoretical Models, Human Movement, 1/f Noise, Point of View, Psychomotor Performance, Psychology and Cognitive Sciences, and Medical and Health Sciences
Previous studies have investigated the comovements of international equity returns by using mean correlations, cointegration, common factor analysis, and other approaches. This paper investigates the evolution of the affinity among major... more
Previous studies have investigated the comovements of international equity returns by using mean correlations, cointegration, common factor analysis, and other approaches. This paper investigates the evolution of the affinity among major euro and non-euro area stock markets in the period 1966-2006 by using distance-based methods for clustering analysis of time series. A periodogram-based metric for mean and squared returns is used to compute distances between the series. This method solves the shortcoming of unequal sample sizes found for different countries. Then, by using dendrogram and multidimensional scaling techniques based on the computed distances, we display clusters for the series of returns and volatilities. The data were divided into two sample periods: previous and subsequent to the introduction of the euro as an electronic currency. For market returns, euro-area countries do not seem to come closer after the introduction of the euro. There is some identity that is main...
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Most of economic and financial time series have a nonstationary behavior. There are different types of nonstationary processes, such as those with stochastic trend and those with deterministic trend. In practice, it can be quite difficult... more
Most of economic and financial time series have a nonstationary behavior. There are different types of nonstationary processes, such as those with stochastic trend and those with deterministic trend. In practice, it can be quite difficult to distinguish between the two processes. In this paper, we compare random walk and determinist trend processes using sample autocorrelation, sample partial autocorrelation and periodogram based metrics.
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The 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... more
The 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, ...
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This 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... more
This 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.
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RESUMO A recente pandemia tornou evidentes para quase todos nós as grandes vantagens do ensino presencial e as grandes limitações do ensino remoto. Mas vale a pena revisitar um pouco as ilusões que estavam por detrás de alguma... more
RESUMO A recente pandemia tornou evidentes para quase todos nós as grandes vantagens do ensino presencial e as grandes limitações do ensino remoto. Mas vale a pena revisitar um pouco as ilusões que estavam por detrás de alguma encomiástica defesa do ensino remoto, pois esse debate, que hoje encontra suporte em dados científicos, pode levar-nos a melhorar tanto o ensino presencial como a minorar inconvenientes do ensino remoto. Essa melhoria é tanto mais importante quanto a pandemia nos trouxe atrasos ou mesmo retrocessos no esforço educativo. Com base em investigação científica muito recente, defende-se neste artigo que a resposta aos inconvenientes da pandemia não pode ser apenas manter os estudantes ocupados e em contacto com a escola e a aprendizagem. A resposta deve ser acelerar o ritmo e a qualidade da educação. Para o fazer, é ainda mais importante prosseguir um currículo exigente e ambicioso e proceder a uma avaliação de resultados frequente e rigorosa. Os meios remotos podem...