Publications
42 results found
Freo M, Luati A, 2024, Lasso-based variable selection methods in text regression: the case of short texts, AStA Advances in Statistical Analysis, Vol: 108, Pages: 69-99, ISSN: 1863-8171
Communication through websites is often characterised by short texts, made of few words, such as image captions or tweets. This paper explores the class of supervised learning methods for the analysis of short texts, as an alternative to unsupervised methods, widely employed to infer topics from structured texts. The aim is to assess the effectiveness of text data in social sciences, when they are used as explanatory variables in regression models. To this purpose, we compare different variable selection procedures when text regression models are fitted to real, short, text data. We discuss the results obtained by several variants of lasso, screening-based methods and randomisation-based models, such as sure independence screening and stability selection, in terms of number and importance of selected variables, assessed through goodness-of-fit measures, inclusion frequency and model class reliance. Latent Dirichlet allocation results are also considered as a term of comparison. Our perspective is primarily empirical and our starting point is the analysis of two real case studies, though bootstrap replications of each dataset are considered. The first case study aims at explaining price variations based on the information contained in the description of items on sale on e-commerce platforms. The second regards open questions in surveys on satisfaction ratings. The case studies are different in nature and representative of different kinds of short texts, as, in one case, a concise descriptive text is considered, whereas, in the other case, the text expresses an opinion.
Luati A, Papagni F, Proietti T, 2024, Efficient nonparametric estimation of generalised autocovariances, Journal of Nonparametric Statistics, Vol: 36, Pages: 23-38, ISSN: 1048-5252
This paper provides a necessary and sufficient condition for asymptotic efficiency of a nonparametric estimator of the generalised autocovariance function of a stationary random process. The generalised autocovariance function is the inverse Fourier transform of a power transformation of the spectral density and encompasses the traditional and inverse autocovariance functions as particular cases. A nonparametric estimator is based on the inverse discrete Fourier transform of the power transformation of the pooled periodogram. We consider two cases: the fixed bandwidth design and the adaptive bandwidth design. The general result on the asymptotic efficiency, established for linear processes, is then applied to the class of stationary ARMA processes and its implications are discussed. Finally, we illustrate that for a class of contrast functionals and spectral densities, the minimum contrast estimator of the spectral density satisfies a Yule–Walker system of equations in the generalised autocovariance estimator.
Catania L, Luati A, 2023, Semiparametric modeling of multiple quantiles, Journal of Econometrics, Vol: 237, ISSN: 0304-4076
We develop a semiparametric model to track a large number of quantiles of a time series. The model satisfies the condition of non-crossing quantiles and the defining property of fixed quantiles. A key feature of the specification is that the updating scheme for time-varying quantiles at each probability level is based on the gradient of the check loss function. Theoretical properties of the proposed model are derived such as weak stationarity of the quantile process and consistency of the estimators of the fixed parameters. The model can be applied for filtering and prediction. We also illustrate a number of possible applications such as: (i) semiparametric estimation of dynamic moments of the observables, (ii) density prediction, and (iii) quantile predictions.
Gorgi P, Lauria CSA, Luati A, 2023, On the optimality of score-driven models, Biometrika, ISSN: 0006-3444
Score-driven models have been recently introduced as a general framework to specify time-varying parameters of conditional densities. %The underlying idea is to specify a time-varying parameter as an autoregressive process with innovation given by the score of the associated log-likelihood. The score enjoys stochastic properties that make these models easy to implement and convenient to apply in several contexts, ranging from biostatistics to finance. Score-driven parameter updates have been shown to be optimal in terms of locally reducing a local version of the Kullback–Leibler divergence between the true conditional density and the postulated density of the model. A key limitation of such an optimality property is that it holds only locally both in the parameter space and sample space, yielding to a definition of local Kullback–Leibler divergence that is in fact not a divergence measure. The current paper shows that score-driven updates satisfy stronger optimality properties that are based on a global definition of Kullback–Leibler divergence. In particular, it is shown that score-driven updates reduce the distance between the expected updated parameter and the pseudo-true parameter. Furthermore, depending on the conditional density and the scaling of the score, the optimality result can hold globally over the parameter space, which can be viewed as a generalization of the monotonicity property of the stochastic gradient descent scheme. Several examples illustrate how the results derived in the paper apply to specific models under different easy-to-check assumptions, and provide a formal method to select the link-function and the scaling of the score.
Abadir KM, Luati A, Paruolo P, 2023, GARCH density and functional forecasts, Journal of Econometrics, Vol: 235, Pages: 470-483, ISSN: 0304-4076
This paper derives the analytic form of the multi-step ahead prediction density for single-period returns, when the latter follow a Gaussian GARCH(1,1) process with a possibly asymmetric news impact curve. The Gaussian density has been used in applications as an approximation of themulti-step ahead prediction density; the analytic form derived here shows that the prediction density, while symmetric, can be far from Gaussian. The explicit form of the prediction density can be used to compute exact tail probabilities and functionals, such as the Value at Risk and the ExpectedShortfall, to quantify expected future required risk capital for single-period returns. Finally, the paper shows how estimation uncertainty can be mapped onto uncertainty regions for any functional of the stated prediction distribution.
DInnocenzo E, Luati A, Mazzocchi M, 2023, A robust score-driven filter for multivariate time series, Econometric Reviews, Vol: 42, Pages: 441-470, ISSN: 0747-4938
A multivariate score-driven filter is developed to extract signals from noisy vector processes. By assuming that the conditional location vector from a multivariate Student’s t distribution changes over time, we construct a robust filter which is able to overcome several issues that naturally arise when modeling heavy-tailed phenomena and, more in general, vectors of dependent non-Gaussian time series. We derive conditions for stationarity and invertibility and estimate the unknown parameters by maximum likelihood. Strong consistency and asymptotic normality of the estimator are derived. Analytical formulae are derived which consent to develop estimation procedures based on a fast and reliable Fisher scoring method. An extensive Monte–Carlo study is designed to assess the finite samples properties of the estimator, the impact of initial conditions on the filtered sequence, the performance when some of the underlying assumptions are violated, such as symmetry of the underlying distribution and homogeneity of the degrees of freedom parameter across marginals. The theory is supported by a novel empirical illustration that shows how the model can be effectively applied to estimate consumer prices from home scanner data.
Proietti T, Luati A, D’Innocenzo E, 2023, Generalized Linear Spectral Models for Locally Stationary Processes, Research Papers in Statistical Inference for Time Series and Related Models: Essays in Honor of Masanobu Taniguchi, Pages: 343-368, ISBN: 9789819908028
A class of parametric models for locally stationary processes is introduced. The class depends on a power parameter that applies to the time-varying spectrum so that it can be locally represented by a (finite low dimensional) Fourier polynomial. The coefficients of the polynomial have an interpretation as time-varying autocovariances, whose dynamics are determined by a linear combination of smooth transition functions, depending on some static parameters. Frequency domain estimation is based on the generalized Whittle likelihood and the pre-periodogram,while model selection is performed through information criteria. Change points are identified via a sequence of score tests. Consistency and asymptotic normality are proved for the parametric estimators considered in the paper, under weak assumptions on the time-varying parameters.
Armillotta M, Luati A, Lupparelli M, 2022, Observation-driven models for discrete-valued time series, Electronic Journal of Statistics, Vol: 16, Pages: 1393-1433, ISSN: 1935-7524
Statistical inference for discrete-valued time series has not been developed like traditional methods for time series generated by continuous random variables. Some relevant models exist, but the lack of a homogenous framework raises some critical issues. For instance, it is not trivial to explore whether models are nested and it is quite arduous to derive stochastic properties which simultaneously hold across different specifications. In this paper, inference for a general class of first order observation-driven models for discrete-valued processes is developed. Stochastic properties such as stationarity and ergodicity are derived under easy-to-check conditions, which can be directly applied to all the models encompassed in the class and for every distribution which satisfies mild moment conditions. Consistency and asymptotic normality of quasi-maximum likelihood estimators are established, with the focus on the exponential family. Finite sample properties and the use of information criteria for model selection are investigated throughout Monte Carlo studies. An empirical application to count data is discussed, concerning a test-bed time series on the spread of an infection.
Ranciati S, Roverato A, Luati A, 2021, Fused graphical lasso for brain networks with symmetries, Journal of the Royal Statistical Society Series C: Applied Statistics, Vol: 70, Pages: 1299-1322, ISSN: 0035-9254
Neuroimaging is the growing area of neuroscience devoted to produce data with the goal of capturing processes and dynamics of the human brain. We consider the problem of inferring the brain connectivity network from time-dependent functional magnetic resonance imaging (fMRI) scans. To this aim we propose the symmetric graphical lasso, a penalized likelihood method with a fused type penalty function that takes into explicit account the natural symmetrical structure of the brain. Symmetric graphical lasso allows one to learn simultaneously both the network structure and a set of symmetries across the two hemispheres. We implement an alternating directions method of multipliers algorithm to solve the corresponding convex optimization problem. Furthermore, we apply our methods to estimate the brain networks of two subjects, one healthy and one affected by mental disorder, and to compare them with respect to their symmetric structure. The method applies once the temporal dependence characterizing fMRI data have been accounted for and we compare the impact on the analysis of different detrending techniques on the estimated brain networks. Although we focus on brain networks, symmetric graphical lasso is a tool which can be more generally applied to learn multiple networks in a context of dependent samples.
Gasperoni F, Luati A, Paci L, et al., 2021, Score-driven modeling of spatio-temporal data, Journal of the American Statistical Association, Vol: 118, Pages: 1066-1077, ISSN: 0162-1459
A simultaneous autoregressive score-driven model with autoregressive disturbances is developed for spatio-temporal data that may exhibit heavy tails. The model specification rests on a signal plus noise decomposition of a spatially filtered process, where the signal can be approximated by a nonlinear function of the past variables and a set of explanatory variables, while the noise follows a multivariate Student-t distribution. The key feature of the model is that the dynamics of the space-time varying signal are driven by the score of the conditional likelihood function. When the distribution is heavy-tailed, the score provides a robust update of the space-time varying location. Consistency and asymptotic normality of maximum likelihood estimators are derived along with the stochastic properties of the model. The motivating application of the proposed model comes from brain scans recorded through functional magnetic resonance imaging when subjects are at rest and not expected to react to any controlled stimulus. We identify spontaneous activations in brain regions as extreme values of a possibly heavy-tailed distribution, by accounting for spatial and temporal dependence.
Luati A, Novelli M, 2021, Explicit-duration Hidden Markov Models for quantum state estimation, COMPUTATIONAL STATISTICS & DATA ANALYSIS, Vol: 158, ISSN: 0167-9473
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- Citations: 1
Catania L, Luati A, 2021, Quasi Maximum Likelihood Estimation of Value at Risk and Expected Shortfall, Econometrics and Statistics
Quasi maximum likelihood estimation of Value at Risk (VaR) and Expected Shortfall (ES) is discussed. The reference likelihood is that of a location-scale asymmetric Laplace distribution, related to a family of loss functions that lead to strictly consistent scoring functions for joint estimation of VaR and ES. The case of zero mean processes is considered, where quasi maximum likelihood estimators (QMLE) are consistent and asymptotically normal, as well as the case of non-zero mean processes, where quasi maximum likelihood estimators lead to inconsistent estimates due to lack of identification. In the latter situation, the asymptotic properties of two stage quasi maximum likelihood estimators (2SQMLE) are derived. QMLE and 2SQMLE are related with sample and M-estimators and compared in terms of asymptotic efficiency. A simulation study investigates the finite sample properties of QMLE, 2SQMLE, sample and M-estimators of expected shortfall.
Luati A, Novelli M, 2020, The Hammersley–Chapman–Robbins inequality for repeatedly monitored quantum system, Statistics & Probability Letters, Vol: 165, Pages: 108852-108852, ISSN: 0167-7152
Catania L, Luati A, 2020, Robust estimation of a location parameter with the integrated Hogg function, STATISTICS & PROBABILITY LETTERS, Vol: 164, ISSN: 0167-7152
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- Citations: 1
Proietti T, Luati A, 2019, GENERALIZED LINEAR CEPSTRAL MODELS FOR THE SPECTRUM OF A TIME SERIES, STATISTICA SINICA, Vol: 29, Pages: 1561-1583, ISSN: 1017-0405
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- Citations: 2
Gasperoni F, Luati A, 2018, Robust methods for detecting spontaneous activations in fMRI data, Pages: 91-110, ISBN: 9783030000387
Functional magnetic resonance imaging (fMRI) is a technique for measuring brain activity. The outcomes of fMRI measurements are complex data that can be interpreted as multivariate time series, recorded at different brain locations, usually across subjects. The literature has been mainly concerned with task-based fMRI analysis, which focuses on the response to controlled exogenous stimuli. Nevertheless, resting state fMRI (RfMRI) analysis, dealing with spontaneous brain activity, is considered the key to understand the neuronal organisation of the brain. The aim of this paper is to identify spontaneous neural activations and to estimate the brain response function in RfMRI data, called Hemodynamic Response Function (HRF). To this purpose, we apply an existing method based on a normality assumption for the data generating process and we consider a novel, more general method, based on robust filtering. Finally, we compare the neural activations and HRF estimates for two specific patients.
Caivano M, Harvey A, Luati A, 2016, Robust time series models with trend and seasonal components, SERIES-JOURNAL OF THE SPANISH ECONOMIC ASSOCIATION, Vol: 7, Pages: 99-120, ISSN: 1869-4187
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- Citations: 11
Luati A, Proietti T, 2016, Generalised partial autocorrelations and the mutual information between past and future, The Fascination of Probability, Statistics and their Applications: In Honour of Ole E. Barndorff-Nielsen, Pages: 303-315, ISBN: 9783319258249
The paper introduces the generalised partial autocorrelation (GPAC) coefficients of a stationary stochastic process. The latter are related to the generalised autocovariances, the inverse Fourier transform coefficients of a power transformation of the spectral density function. By interpreting the generalised partial autocorrelations as the partial autocorrelation coefficients of an auxiliary process, we derive their properties and relate them to essential features of the original process. Based on a parameterisation suggested by [1] and on Whittle likelihood, we develop an estimation strategy for the GPAC coefficients.We further prove that the GPAC coefficients can be used to estimate the mutual information between the past and the future of a time series.
Proietti T, Luati A, 2015, Generalized linear spectral models, Unobserved Components and Time Series Econometrics, Publisher: Oxford University PressOxford, Pages: 331-347, ISBN: 0199683662
<jats:title>Abstract</jats:title><jats:p>This chapter considers a class of parametric spectrum estimators based on a generalized linear model for exponential random variables with power link. The power transformation of the spectrum of a stationary process can be expanded in a Fourier series, with the coefficients representing generalized autocovariances. Direct Whittle estimation of the coefficients is generally unfeasible, as they are subject to constraints. The problem can be overcome using an ARMA representation for the power transformation of the spectrum. Estimation is carried out by maximizing the Whittle likelihood, whereas spectral model selection, as a function of the power transformation parameter and the ARMA orders, can be by information criteria. The proposed methods are applied to the estimation of the inverse autocorrelation function and the related problem of selecting the optimal interpolator, and for the identification of spectral peaks. More generally, they can be applied to spectral estimation with possibly misspecified models.</jats:p>
Donatelli M, Luati A, Martinelli A, 2015, Spectral filtering for trend estimation, LINEAR ALGEBRA AND ITS APPLICATIONS, Vol: 473, Pages: 217-235, ISSN: 0024-3795
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- Citations: 1
Proietti T, Luati A, 2015, The generalised autocovariance function, JOURNAL OF ECONOMETRICS, Vol: 186, Pages: 245-257, ISSN: 0304-4076
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- Citations: 7
Harvey A, Luati A, 2014, Filtering With Heavy Tails, JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION, Vol: 109, Pages: 1112-1122, ISSN: 0162-1459
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- Citations: 59
Kontoghiorghes EJ, Van Dijk HK, Belsley DA, et al., 2014, CFEnetwork: The Annals of computational and financial econometrics: 2nd issue
Proietti T, Luati A, 2013, Maximum likelihood estimation of time series models: the Kalman filter and beyond, Handbook of Research Methods and Applications in Empirical Macroeconomics, Publisher: Edward Elgar Publishing, ISBN: 9780857931016
Luati A, Proietti T, Reale M, 2012, The Variance Profile, JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION, Vol: 107, Pages: 607-621, ISSN: 0162-1459
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- Citations: 4
Dagum E, Luati A, 2012, Asymmetric Filters for Trend-Cycle Estimation, Economic Time Series, Publisher: Chapman and Hall/CRC, Pages: 213-230
Luati A, Proietti T, 2011, On the equivalence of the weighted least squares and the generalised least squares estimators, with applications to kernel smoothing, Annals of the Institute of Statistical Mathematics, Vol: 63, Pages: 851-871, ISSN: 0020-3157
This paper establishes the conditions under which the generalised least squares estimator of the regression parameters is equivalent to the weighted least squares estimator. The equivalence conditions have interesting applications in local polynomial regression and kernel smoothing. Specifically, they enable to derive the optimal kernel associated with a particular covariance structure of the measurement error, where optimality has to be intended in the Gauss-Markov sense. For local polynomial regression it is shown that there is a class of covariance structures, associated with non-invertible moving average processes of given orders which yield the Epanechnikov and the Henderson kernels as the optimal kernels. © 2009 The Institute of Statistical Mathematics, Tokyo.
Luati A, 2011, An approximate quantum Cramer-Rao bound based on skew information, BERNOULLI, Vol: 17, Pages: 628-642, ISSN: 1350-7265
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- Citations: 1
Proietti T, Luati A, 2011, Low-pass filter design using locally weighted polynomial regression and discrete prolate spheroidal sequences, JOURNAL OF STATISTICAL PLANNING AND INFERENCE, Vol: 141, Pages: 831-845, ISSN: 0378-3758
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- Citations: 5
Luati A, Proietti T, 2010, ON THE SPECTRAL PROPERTIES OF MATRICES ASSOCIATED WITH TREND FILTERS, ECONOMETRIC THEORY, Vol: 26, Pages: 1247-1261, ISSN: 0266-4666
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- Citations: 5
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