1,720,976 research outputs found
Una proposta per la individuazione e la correzione di dati anomali in serie temporali: applicazione ai dati del fatturato delle imprese industriali
No full textOutliers in Time Series: an Empirical Likelihood Approach
No full textThe empirical likelihood method is known to be a flexible and effective
approach for testing hypotheses and constructing confidence regions in a nonparametric
setting. This framework is adopted here for dealing with the outlier problem
in time series where conventional distributional assumptions may be inappropriate
in most cases. The procedure is illustrated by a simulation experiment
Data-driven portmanteau tests for time series
No full textPortmanteau tests and information criteria are widely used for checking the hypothesis of independence in time series. More recently, data-driven versions were proposed, where the tests are calibrated based on the largest estimated autocorrelation. It seems natural to introduce a double test statistic (M, Q) where Q is the portmanteau and M is the largest squared autocorrelation. Both statistics have been investigated at length in the past decades. We computed under reasonable assumptions the bivariate probability distribution of this double statistic, conditional, in addition, to the lag at which the largest autocorrelation is found. Tests of the null hypothesis of independence based on rejection regions in the plane (M, Q) are proposed, and some methods to select the rejection region in order to maximize power when the alternative hypothesis is unknown are suggested. A simulation study and a thorough comparison with some popular tests have been performed to show the advantages of our proposal. Notice that this latter includes some well-known univariate tests, so we could expect not only an optimal choice but also additional information which may turn useful for a better understanding of the time series for both model building and forecasting
A simple portmanteau test with data-driven truncation point
No full textTime series forecasting is an important application of many statistical methods. When it is appropriate to assume that the data may be projected towards the future based on the past history of the dataset, a preliminary examination is usually required to ensure that the data sequence is autocorrelated. This is a quite obvious assumption that has to be made and can be the object of a formal test of hypotheses. The most widely used test is the portmanteau test, i.e., a sum of the squared standardized autocorrelations up to an appropriate maximum lag (the truncation point). The choice of the truncation point is not obvious and may be data-driven exploiting supplementary information, e.g. the largest autocorrelation and the lag where such maximum is found. In this paper, we propose a portmanteau test with a truncation point equal to the lag of the largest (absolute value) estimated autocorrelation. Theoretical and simulation-based comparisons based on size and power are performed with competing portmanteau tests, and encouraging results are obtained
Data-driven portmanteau tests for time series
No full textPortmanteau tests and information criteria are widely used for checking the hypothesis of independence in time series. More recently, data-driven versions were proposed, where the tests are calibrated based on the largest estimated autocorrelation. It seems natural to introduce a double test statistic (M, Q) where Q is the portmanteau and M is the largest squared autocorrelation. Both statistics have been investigated at length in the past decades. We computed under reasonable assumptions the bivariate probability distribution of this double statistic, conditional, in addition, to the lag at which the largest autocorrelation is found. Tests of the null hypothesis ofindependence based on rejection regions in the plane (M, Q) are proposed, and some methods to select the rejection region in order to maximize power when the alternative hypothesis is unknown are suggested. A simulation study and a thorough comparison with some popular tests have been performed to show the advantages of our proposal. Notice that this latter includes some well-known univariate tests, so we could expect not only an optimal choice but also additional information which may turn useful for a better understanding of the time series for both model building and forecasting
Unsupervised classification of texture images by gray-level spatial dependence matrices and genetic algorithms
No full textRecognition of objects and regions of interest in digital image processing
often relies on texture classification. The source image is divided according to a
rectangular grid to form textured regions each of which is characterized by some
numerical significant measure called feature. A new approach is introduced that uses
the gray-level spatial dependence matrices and the genetic clustering with unknown
K algorithms to locate sets of homogeneous regions and enhance the discrimination
amongst them. There is no need to select and compute complicated features
transforms as the procedure is based on the optimal weighting of the simple basic
features. A simulation experiment is performed using the well-known Brodatz
textures to demonstrate that the new procedure is able to define well separated clusters
according to the principle of strong internal cohesion and high inter-clusters
separation
Periodic autoregressive models for time series with integrated seasonality
No full textA comprehensive seasonally integrated periodic autoregressive model is suggested which is shown to be flexible enough to include both the stochastic seasonal integrated and random trigonometric polynomial-based models. The demonstration of the equivalence between the two approaches is the objective of two theorems that are stated and proved in some details. A nice advantage of our model building procedure is that it is able to provide the user not only with a detailed model for data description and forecasting purpose but in addition with a hint at the presence of seasonal unit roots. The model which is illustrated in the present paper may be considered parsimonious, i.e. the number of estimated parameters, for a given goodness-of-fit criterion, is taken as low as possible, in two ways. First, by imposing unit roots and seasonal unit roots so that some estimated parameters are replaced by a differencing operator with fixed coefficients, and, second, by adopting a subset periodic autoregressive model, so that some parameters do not need to be estimated as they are constrained to equal zero. The effectiveness of our model is highlighted by an extensive simulation experiment that supports our claim that the model building procedure described here may be of good use as well for checking the existence of seasonal unit roots. Applications to real-world time series data sets are reported, and promising results are obtained that allow us to suggest that the seasonally integrated periodic autoregressive model may be safely used for modelling a wide range of seasonal time series data. In addition, well-known widely used tests, such as HEGY and the Taylor variance ratio test, are shown to provide us with results that generally agree with our findings
Periodic Autoregressive Models for Stochastic Seasonality
No full textBook cover
Mathematical and Statistical Methods for Actuarial Sciences and Finance pp 79–85Cite as
Periodic Autoregressive Models for Stochastic Seasonality
Roberto Baragona, Francesco Battaglia & Domenico Cucina
Conference paper
First Online: 14 December 2021
238 Accesses
Abstract
The periodic autoregressive (PAR) models for seasonal time series data seem able to take into account simultaneously many issues, e.g. the mean level and the second order moments. The problem naturally arises if seasonal unit roots have to be imposed on the model structure for taking into account stochastic seasonality. Statistical tests for the presence of seasonal unit roots have been developed, but in this environment they may suffer from some drawbacks. The approach can be advantageously reversed, that is the attention may focus on model building in the first place, then the goodness of fit may be checked according to some suitable criterion. The effectiveness of the suggested procedure has been confirmed by a comprehensive simulation study that includes a comparison with some well-known widely used seasonal unit roots tests. An application to the monthly Italian general industrial production index (1993–2016) is also presented
Empirical likelihood ratio in penalty form and the convex hull problem
No full textThe empirical likelihood ratio is not defined when the null vector does not
belong to the convex hull of the estimating functions computed on the data. This may
happen with non-negligible probability when the number of observations is small and
the dimension of the estimating functions is large: it is called the convex hull problem.
Several modifications have been proposed to overcome such drawback: the penalized,
the adjusted, the balanced and the extended empirical likelihoods, though they yield
different values from the ordinary empirical likelihood in all cases. The convex hull
problem is addressed here in the framework of nonlinear optimization, proposing to
follow the penalty method. A generalized empirical likelihood in penalty form is considered,
and all the proposed modifications are shown to be in that form. We propose
simple penalty forms of the empirical likelihood, whose values are equal to those of
the ordinary empirical likelihood when the convex hull condition is satisfied. A comparison
by simulation and real data is included. All proofs and additional simulation
results appear in the Supplementary Material
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