Scientist

A fragmented-periodogram approach for clustering big data time series.

Advances in Data Analysis and Classification, 2019

Jorge Caiado, Nuno Crato, Pilar Poncela.

Received: 6 September 2018 / Revised: 2 June 2019 / Accepted: 5 June 2019© The Author(s) 2019

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 regularization 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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O Eclipse da Relatividade

Revista da Ciência Elementar, Outubro 2019.

Nuno Crato e Luis Tirapicos

Há na história da ciência algumas datas que marcam revoluções no nosso conhecimento do Universo. O ano de 1666 constitui, certamente, uma dessas datas. Foi então que Isaac Newton, na altura com 23 anos, criou o cálculo integral e diferencial, a teoria da gravitação universal e a teoria das cores. O ano de 1905, em que Einstein publicou quatro trabalhos revolucionários, constitui uma outra dessas datas-chave. E deve-se a este físico ainda uma outra data-chave: o ano de 1915, em que formulou a teoria da relatividade geral, por vezes considerada a criação científica mais fabulosa da mente humana.

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Assessment Background: What PISA Measures and How

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Luísa Araújo, Patrícia Costa and Nuno Crato

November, 2020

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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Tests for comparing time series of unequal lengths

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Journal of Statistical Computation and Simulation, Maio 2011.

Jorge Caiado, Nuno Crato and Daniel Peña.

This paper deals with hypothesis testing for independent time series with unequal length. It proposes a spectral test based on the distance between the periodogram ordinates and a parametric test based on the distance between the parameter estimates of fitted autoregressive moving average models. Both tests are compared with a likelihood ratio test based on the pooled spectra. In all cases, the null hypothesis is that the two series under consideration are generated by the same stochastic process. The performance of the three tests is investigated by a Monte Carlo simulation study.

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