Nuno Crato

University of Lisbon, ISEG, Department of Mathematics, Professor

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Nuno 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.

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Supervisors: Ph.D. Advisor (1992): Howard M. Taylor, University of Delaware
Address: ISEG, Rua Miguel Lupi 20
1200-781 Lisboa
Portugal

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Research Papers by Nuno Crato

New tests for stationarity and parity reversion: Evidence on New Zealand real exchange rates

Empirical Economics, 1995

The present paper discusses the stochastic stationarity of New Zealand exchange rates in light of... 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.

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Aplicações de Modelos de Memória Longa

Forecasting business and economic time series with overdifferenced models

Portuguese Journal of Management Studies, 1993

Memory in Returns and Volatilities of Commodity Futures Contracts

Abstract: Various authors claim to have found evidence of stochastic long memory behavior in futu... more Abstract: Various authors claim to have found evidence of stochastic long memory behavior in futures&#x27; contract returns using the Hurst statistic. This paper reexamines futures&#x27; returns for evidence of persistent behavior using a biased-corrected version of the Hurst statistic and an ...

Discrimination between deterministic trend and stochastic trend processes

Most of economic and financial time series have a nonstationary behavior. There are different typ... 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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Stationary persistent time series misspecified as nonstationary ARIMA

Stat Pap, 1996

Long-memory processes, such as Autoregressive Fractionally Integrated Moving-Average processes—AR... 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.

A fragmented-periodogram approach for clustering big data time series

Advances in Data Analysis and Classification, 2019

We propose and study a new frequency-domain procedure for characterizing and comparing large sets... 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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A periodogram-based metric for time series classification

by Nuno Crato and Jorge Caiado

The statistical discrimination and clustering literature has studied the problem of identifying s... more The statistical discrimination and clustering literature has studied the problem of identifying similarities in time series data. Some studies use non-parametric approaches for splitting a set of time series into clusters by looking at their Euclidean distances in the space of points. A new measure of distance between time series based on the normalized periodogram is proposed. Simulation results comparing this measure with others parametric and non-parametric metrics are provided. In particular , the classification of time series as stationary or as non-stationary is discussed. The use of both hierarchical and non-hierarchical clustering algorithms is considered. An illustrative example with economic time series data is also presented.

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Journal of Statistical Computation and Simulation Tests for comparing time series of unequal lengths Tests for comparing time series of unequal lengths

by Daniel Peña, Nuno Crato, and Jorge Caiado

This paper deals with hypothesis testing for independent time series with unequal length. It prop... more 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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A GARCH-based method for clustering of financial time series: International stock markets evidence

by Jorge Caiado and Nuno Crato

Recent Advances in Stochastic Modeling and Data Analysis, 2007

In this paper, we introduce a volatility-based method for clustering analysis of …nancial time se... more In this paper, we introduce a volatility-based method for clustering analysis of …nancial 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 di¤erent lengths. As an illustrative example, we investigate the similarities among major international stock markets using daily return series with di¤erent sample sizes from 1966 to 2006. From cluster analysis, most European markets countries, United States and Canada appear close together, and most Asian/Paci…c 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.

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Estimation of the maximal moment exponent with censored data

Communications in Statistics - Simulation and Computation, 2000

Heavy-tailed distributions have been used to model phenomena in which extreme events occur with h... more Heavy-tailed distributions have been used to model phenomena in which extreme events occur with high probability. In these type of occurrences, it is likely that extreme events are not observable after a certain threshold. Appropriate estimators are needed to deal with this type of censored data. We show that the well-known Hill-Hall estimator is unable to deal with censored data and yields highly biased estimates. We propose and study an unbiased modified maximum likelihood estimator, as well as a truncated tail regression estimator. We assess the expected value and the variance of these estimators in the cases of stable-and Pareto-distributed data.

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Some problems in the overspecification of ARMA and ARIMA processes using ARFIMA models

Nonstationary ARIMA processes and nearly nonstationary ARMA pro-cesses, such as autoregressive pr... 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.

Parameterized estimation of long-range correlation and variance components in human serial interval production

Motor Control, 2010

Repetitive movements lead to isochronous serial interval production which exhibit inherent variab... more Repetitive movements lead to isochronous serial interval production which exhibit inherent variability. The Wing-Kristofferson model offers a decomposition of the interresponse intervals in tapping tasks based on a cognitive component and on a motor component. We suggest a new theoretical and fully parametric approach to this model in which the cognitive component is modeled as a long-memory process and the motor component is treated as a white noise process, mutually independent. Under these assumptions, we obtained the autocorrelation function and the spectral density function. Furthermore, we propose an estimator based on the maximization of the frequency-domain representation of the likelihood function. Finally, we conducted a simulation study to assess the properties of this estimator and performed an experimental study involving tapping tasks with two target frequencies (1.250 Hz and 0.625 Hz).

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On the power of underdifferencing and overdifferencing tests against nearly nonstationary alternatives

Commun Statist Simulat Comput, 1997

The choice of the appropriate degree of integration is a very important question in ARIMAtime ser... 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

Measuring Hysteresis in Unemployment Rates with Long Memory Models

We address the question of unemployment hysteresis within the context of ARFIMA models. Our resul... more

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On the Detection and Estimation of Long Memory in Stochastic Volatility

by Nuno Crato and F. Breidt

Long-Range Dependence in the Conditional Variance of Stock Returns

We examine persistence in the conditional variance of U.S. stock returns indexes. Our results sho... more We examine persistence in the conditional variance of U.S. stock returns indexes. Our results show evidence of long memory in high-frequency data, suggesting that models of conditional heteroskedasticity should be made flexible enough to accommodate these empirical findings. JEL classification : C22 * Corresponding author SSDI 0165-1765(94)00430-A 282 N. Crato, P.J.F. de Lima I Economics Letters 45 (1994) 281-285

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Identifying the evolution of stock markets stochastic structure after the euro

by Jorge Caiado and Nuno Crato

Mpra Paper, 2008

Previous studies have investigated the comovements of international equity markets by using corre... 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 in order to compute distances between the stock markets. This method captures the stochastic dependence structure of the time series and solves the shortcoming of unequal sample sizes found for di¤erent countries. The clusters of countries are formed by the dendrogram and the principal coordinates associated with the sample spectrum for both the series of returns and volatilities. The empirical results suggest that the cross-country groups have become considerably more homogeneous with the introduction of the euro as an electronic currency. For reference, we also explore the pairwise correlations among the series.

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Long memory and nonstationarity in time perception models

45Th Scientific Meeting of the Italian Statistical Society, May 8, 2010

Experimentalists have found stationary long non-periodic waves in human controlled rhythmic movem... more

Tests for comparing time series of unequal lengths

by Nuno Crato and Daniel Pena

Http Dx Doi Org 10 1080 00949655 2011 592985, Nov 9, 2012

Nuno Crato

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