14,121 research outputs found
Multivariate analysis in vector time series
This paper reviews the applications of classical multivariate techniques for discrimination, clustering and dimension reduction for time series data. It is shown that the discrimination problem can be seen as a model selection problem. Some of the results obtained in the time domain are reviewed. Clustering time series requires the definition of an adequate metric between univariate time series and several possible metrics are analyzed. Dimension reduction has been a very active line of research in the time series literature and the dynamic principal components or canonical analysis of Box and Tiao (1977) and the factor model as developed by Peña and Box (1987) and Peña and Poncela (1998) are analyzed. The relation between the nonstationary factor model and the cointegration literature is also reviewed
Model selection criteria and quadratic discrimination in ARMA and SETAR time series models
We show that analyzing model selection in ARMA time series models as a quadratic discrimination problem provides a unifying approach for deriving model selection criteria. Also this approach suggest a different definition of expected likelihood that the one proposed by Akaike. This approach leads to including a correction term in the criteria which does not modify their large sample performance but can produce significant improvement in the performance of the criteria in small samples. Thus we propose a family of criteria which generalizes the commonly used model selection criteria. These ideas can be extended to self exciting autoregressive models (SETAR) and we generalize the proposed approach for these non linear time series models. A Monte-Carlo study shows that this family improves the finite sample performance of criteria such as AIC, corrected AIC and BIC, for ARMA models, and AIC, corrected AIC, BIC and some cross-validation criteria for SETAR models. In particular, for small and medium sample size the frequency of selecting the true model improves for the consistent criteria and the root mean square error of prediction improves for the efficient criteria. These results are obtained for both linear ARMA models and SETAR models in which we assume that the threshold and the parameters are unknown
Bijectiveness of the Nash Map for Quasi-Ordinary Hypersurface Singularities
In this paper we give a positive answer to a question of Nash concerning the
arc space of a singularity, for the class of quasi-ordinary hypersurface
singularities, extending to this case previous results and techniques of
Shihoko Ishii.Comment: comments and references adde
Toric embedded resolutions of quasi-ordinary hypersurface singularities
We build two embedded resolution procedures of a quasi-ordinary singularity
of complex analytic hypersurface, by using toric morphisms which depend only on
the characteristic monomials associated to a quasi-ordinary projection of the
singularity. This result answers an open problem of Lipman in Equisingularity
and simultaneous resolution of singularities, Resolution of Singularities,
Progress in Mathematics No. 181, 2000, 485-503. In the first procedure the
singularity is embedded as hypersurface. In the second procedure, which is
inspired by a work of Goldin and Teissier for plane curves (see Resolving
singularities of plane analytic branches with one toric morphism,loc. cit.,
pages 315-340), we re-embed the singularity in an affine space of bigger
dimension in such a way that one toric morphism provides its embedded
resolution. We compare both procedures and we show that they coincide under
suitable hypothesis.Comment: To apear in Annales de l'Institut Fourier (Grenoble
A note on prediction and interpolation errors in time series
In this note we analyze the relationship between one-step ahead prediction errors and interpolation errors in time series. We obtain an expression of the prediction errors in terms of the interpolation errors and then we show that minimizing the sum of squares of the one step-ahead standardized prediction errors is equivalent to minimizing the sum of squares of standardized interpolation errors
F-threshold functions: syzygy gap fractals and the two-variable homogeneous case
In this article we study F-pure thresholds (and, more generally,
F-thresholds) of homogeneous polynomials in two variables over a field of
characteristic p>0. Passing to a field extension, we factor such a polynomial
into a product of powers of pairwise prime linear forms, and to this collection
of linear forms we associate a special type of function called a syzygy gap
fractal. We use this syzygy gap fractal to study, at once, the collection of
all F-pure thresholds of all polynomials constructed with the same fixed linear
forms. This allows us to describe the structure of the denominator of such an
F-pure threshold, showing in particular that whenever the F-pure threshold
differs from its expected value its denominator is a multiple of p. This
answers a question of Schwede in the two-variable homogeneous case. In
addition, our methods give an algorithm to compute F-pure thresholds of
homogenous polynomials in two variables.Comment: 42 pages; 6 figures. Section 6 was mostly rewritten; a new appendix
was included; other smaller changes throughout. Comments welcom
Variance changes detection in multivariate time series
This paper studies the detection of step changes in the variances and in the correlation structure of the components of a vector of time series. Two procedures are considered. The first is based on the likelihood ratio test and the second on cusum statistics. These two procedures are compared in a simulation study and we conclude that the cusum procedure is more powerful. The procedures are illustrated in two examples.
MULTIVARIATE ANALYSIS IN VECTOR TIME SERIES
This paper reviews the applications of classical multivariate techniques for discrimination, clustering and dimension reduction for time series data. It is shown that the discrimination problem can be seen as a model selection problem. Some of the results obtained in the time domain are reviewed. Clustering time series requires the definition of an adequate metric between univariate time series and several possible metrics are analyzed. Dimension reduction has been a very active line of research in the time series literature and the dynamic principal components or canonical analysis of Box and Tiao (1977) and the factor model as developed by Peña and Box (1987) and Peña and Poncela (1998) are analyzed. The relation between the nonstationary factor model and the cointegration literature is also reviewed.
VARIANCE CHANGES DETECTION IN MULTIVARIATE TIME SERIES
This paper studies the detection of step changes in the variances and in the correlation structure of the components of a vector of time series. Two procedures are considered. The first is based on the likelihood ratio test and the second on cusum statistics. These two procedures are compared in a simulation study and we conclude that the cusum procedure is more powerful. The procedures are illustrated in two examples.R
A NOTE ON PREDICTION AND INTERPOLATION ERRORS IN TIME SERIES
In this note we analyze the relationship between one-step ahead prediction errors and interpolation errors in time series. We obtain an expression of the prediction errors in terms of the interpolation errors and then we show that minimizing the sum of squares of the one step-ahead standardized prediction errors is equivalent to minimizing the sum of squares of standardized interpolation errors.
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