1,720,991 research outputs found
Goodness-of-fit tests in the Cox proportional hazards model
No full textWe consider a variety of tests for testing goodness-of-fit in a parametric Cox proportional hazards (PH) model and compare their performance. Aspects of the model under test include the baseline distribution and time-invariance of covariates. We also test for the PH model itself against a certain generalization. This is done through an extensive Monte Carlo study where we simulate the performance of the tests for these three paired hypotheses. The results show that the tests based on the empirical characteristic function and those based on the empirical Laplace transform have the best overall power performance. It is also found that the distributions of the considered test statistics do not depend on the specific functional form of the covariate functio
Goodness-of-fit tests in conditional duration models
No full textWe propose specification tests for the innovation distribution in conditional duration models. The new tests are based either on the cumulative distribution function, or on exponential transforms such as the Laplace transform and the characteristic function, or on characterizations of the innovation-distribution under test. We study the finite-sample performance of the proposed procedures in comparison with alternative tests which employ nonparametric density estimates as well as with tests based on entropy. A bootstrap version of the tests is utilized in order to study the small sample behavior of the procedures. A real-data example illustrates the applicability of our method and confirms conclusions drawn by earlier author
Change-point methods for multivariate time-series: paired vectorial observations
No full textWe consider paired and two-sample break-detection procedures for vectorial observations and multivariate time series. The new methods involve L2-type criteria based on empirical characteristic functions and are easy to compute regardless of dimension. We obtain asymptotic results that allow for application of the methods to a wide range of settings involving on-line as well as retrospective circumstances with dependence between the two time series as well as with dependence within each series. In the ensuing Monte Carlo study the new detection methods are implemented by means of resampling procedures which are properly adapted to the type of data at hand, be it independent or paired, autoregressive or GARCH structured, medium or heavy-tailed. The new methods are also applied on a real dataset from the financial sector over a time period which includes the Brexit referendu
Two-sample tests for multivariate functional data
No full textWe consider two–sample tests for functional data with observations which may be uni– or multi–dimensional. The new methods are formulated as L2–type criteria based on empirical characteristic functions and are convenient from the computational point of vie
Goodness-of-fit tests for parametric specifications of conditionally heteroscedastic models
No full textWe consider a goodness-of-fit test for certain parametrizations of conditionally heteroscedastic time series with unobserved components. Our test is quite general in that it can be employed to validate any given specification of arbitrary order and may even be invoked for testing not just GARCH models but also some related models such as autoregressive conditional duration models. The test statistic utilizes the characterization of Bierens (J Econom 20:105–134, 1982) and may be written down in a convenient closed-form expression. Consistency of the test is proved, and the asymptotic distribution of the test statistic under the null hypothesis is studied. Since this distribution depends on unknown quantities, two bootstrap resampling schemes are investigated and compared in order to approximate critical points and actually carry out the test. Finite-sample results are presented as well as applications of the proposed procedures to real data from the financial market
Testing serial independence with functional data
No full textWe consider tests of serial independence for a sequence of functional observations. The new methods are formulated as L2-type criteria based on empirical characteristic functions and are convenient from the computational point of view. We derive asymptotic normality of the proposed test statistics for both discretely and continuously observed functions. In a Monte Carlo study, we show that the new test is sensitive with respect to functional GARCH alternatives, investigate the choice of necessary tuning parameters, and demonstrate that critical values obtained by resampling lead to a test with good performance in any setup, whereas the asymptotic critical values may be recommended only for a sufficiently fine discretization grid. Finite-sample comparison with a distance (auto)covariance test criterion is also included, and the article concludes with application on a real data se
Asymptotics, finite-sample comparisons and applications for two-sample tests with functional data
No full textWe consider two-sample tests for functional data with observations which may be uni- or multi-dimensional. The new methods are formulated as -type criteria based on empirical characteristic functions and are convenient from the computational point of view. Asymptotic properties are presented. Simulations and two real data applications are conducted in order to evaluate the performance of the proposed tests vis-à-vis other method
Tests for structural changes in time series of counts
No full textWe propose methods for detecting structural changes in time series with discrete-valued observations. The detector statistics come in familiar L2-type formulations incorporating the empirical probability generating function. Special emphasis is given to the popular models of integer autoregression and Poisson autoregression. For both models, we study mainly structural changes due to a change in distribution, but we also comment for the classical problem of parameter change. The asymptotic properties of the proposed test statistics are studied under the null hypothesis as well as under alternatives. A Monte Carlo power study on bootstrap versions of the new methods is also included along with a real data exampl
Comments on: Tests for multivariate normalit: a critical review with emphasis on weighted L2 -statistics
No full textWe discuss extension of the BHEP test to more general families of distribution
Characteristic function-based inference for GARCH models with heavy-tailed innovations
No full textWe consider estimation and goodness-of-fit tests in GARCH models with innovations following a heavy-tailed and possibly asymmetric distribution. Although the method is fairly general and applies to GARCH models with arbitrary innovation distribution, we consider as special instances the stable Paretian, the variance gamma, and the normal inverse Gaussian distribution. Exploiting the simple structure of the characteristic function of these distributions, we propose minimum distance estimation based on the empirical characteristic function of properly standardized GARCH-residuals. The finite-sample results presented facilitate comparison with existing methods, while the new procedures are also applied to real data from the financial marke
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